F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag.

Example 1

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 1)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(26.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(5\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=6 \]

The velocity after \(5\) seconds is approximately \(1.59\) meters per second.

Example 2

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 2)

A mass of \(9\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(22.8\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 9v'=-0.91v^2 \hspace{3em} v(0)=5 \]

The velocity after \(2\) seconds is approximately \(2.49\) meters per second.

Example 3

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 3)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(8\) meters per second, experiencing an initial air resistance of \(22.4\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=8 \]

The velocity after \(8\) seconds is approximately \(1.46\) meters per second.

Example 4

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 4)

A mass of \(6\) kg is thrown horizontally with an initial velocity of \(4\) meters per second, experiencing an initial air resistance of \(7.36\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 6v'=-0.46v^2 \hspace{3em} v(0)=4 \]

The velocity after \(3\) seconds is approximately \(2.08\) meters per second.

Example 5

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 5)

A mass of \(2\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(5.04\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 2v'=-0.14v^2 \hspace{3em} v(0)=6 \]

The velocity after \(3\) seconds is approximately \(2.65\) meters per second.

Example 6

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 6)

A mass of \(9\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(73.7\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(4\) seconds.

Answer.

The IVP is given by

\[ 9v'=-0.91v^2 \hspace{3em} v(0)=9 \]

The velocity after \(4\) seconds is approximately \(1.94\) meters per second.

Example 7

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 7)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(8\) meters per second, experiencing an initial air resistance of \(47.4\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=8 \]

The velocity after \(6\) seconds is approximately \(1.47\) meters per second.

Example 8

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 8)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(59.9\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=9 \]

The velocity after \(6\) seconds is approximately \(1.50\) meters per second.

Example 9

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 9)

A mass of \(6\) kg is thrown horizontally with an initial velocity of \(4\) meters per second, experiencing an initial air resistance of \(7.36\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 6v'=-0.46v^2 \hspace{3em} v(0)=4 \]

The velocity after \(6\) seconds is approximately \(1.41\) meters per second.

Example 10

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 10)

A mass of \(9\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(22.8\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(5\) seconds.

Answer.

The IVP is given by

\[ 9v'=-0.91v^2 \hspace{3em} v(0)=5 \]

The velocity after \(5\) seconds is approximately \(1.42\) meters per second.

Example 11

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 11)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(8.75\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=5 \]

The velocity after \(3\) seconds is approximately \(2.44\) meters per second.

Example 12

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 12)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(12.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(5\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=6 \]

The velocity after \(5\) seconds is approximately \(1.94\) meters per second.

Example 13

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 13)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(15.4\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=9 \]

The velocity after \(2\) seconds is approximately \(4.21\) meters per second.

Example 14

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 14)

A mass of \(2\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(1.26\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(9\) seconds.

Answer.

The IVP is given by

\[ 2v'=-0.14v^2 \hspace{3em} v(0)=3 \]

The velocity after \(9\) seconds is approximately \(1.04\) meters per second.

Example 15

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 15)

A mass of \(7\) kg is thrown horizontally with an initial velocity of \(7\) meters per second, experiencing an initial air resistance of \(28.9\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 7v'=-0.59v^2 \hspace{3em} v(0)=7 \]

The velocity after \(3\) seconds is approximately \(2.53\) meters per second.

Example 16

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 16)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(12.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=6 \]

The velocity after \(2\) seconds is approximately \(3.26\) meters per second.

Example 17

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 17)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(8.75\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(5\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=5 \]

The velocity after \(5\) seconds is approximately \(1.82\) meters per second.

Example 18

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 18)

A mass of \(9\) kg is thrown horizontally with an initial velocity of \(4\) meters per second, experiencing an initial air resistance of \(14.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 9v'=-0.91v^2 \hspace{3em} v(0)=4 \]

The velocity after \(6\) seconds is approximately \(1.17\) meters per second.

Example 19

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 19)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(28.3\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(9\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=9 \]

The velocity after \(9\) seconds is approximately \(1.35\) meters per second.

Example 20

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 20)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(7\) meters per second, experiencing an initial air resistance of \(17.2\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=7 \]

The velocity after \(6\) seconds is approximately \(1.78\) meters per second.

Example 21

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 21)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(2\) meters per second, experiencing an initial air resistance of \(0.760\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=2 \]

The velocity after \(3\) seconds is approximately \(1.45\) meters per second.

Example 22

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 22)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(6.50\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=5 \]

The velocity after \(3\) seconds is approximately \(2.53\) meters per second.

Example 23

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 23)

A mass of \(2\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(1.26\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 2v'=-0.14v^2 \hspace{3em} v(0)=3 \]

The velocity after \(3\) seconds is approximately \(1.84\) meters per second.

Example 24

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 24)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(28.3\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(4\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=9 \]

The velocity after \(4\) seconds is approximately \(2.56\) meters per second.

Example 25

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 25)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(8\) meters per second, experiencing an initial air resistance of \(22.4\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(9\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=8 \]

The velocity after \(9\) seconds is approximately \(1.32\) meters per second.

Example 26

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 26)

A mass of \(9\) kg is thrown horizontally with an initial velocity of \(7\) meters per second, experiencing an initial air resistance of \(44.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 9v'=-0.91v^2 \hspace{3em} v(0)=7 \]

The velocity after \(2\) seconds is approximately \(2.90\) meters per second.

Example 27

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 27)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(8\) meters per second, experiencing an initial air resistance of \(12.2\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(9\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=8 \]

The velocity after \(9\) seconds is approximately \(1.44\) meters per second.

Example 28

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 28)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(28.3\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=9 \]

The velocity after \(8\) seconds is approximately \(1.49\) meters per second.

Example 29

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 29)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(26.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(4\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=6 \]

The velocity after \(4\) seconds is approximately \(1.86\) meters per second.

Example 30

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 30)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(8\) meters per second, experiencing an initial air resistance of \(16.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=8 \]

The velocity after \(2\) seconds is approximately \(3.92\) meters per second.

Example 31

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 31)

A mass of \(2\) kg is thrown horizontally with an initial velocity of \(7\) meters per second, experiencing an initial air resistance of \(6.86\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 2v'=-0.14v^2 \hspace{3em} v(0)=7 \]

The velocity after \(6\) seconds is approximately \(1.78\) meters per second.

Example 32

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 32)

A mass of \(6\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(16.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 6v'=-0.46v^2 \hspace{3em} v(0)=6 \]

The velocity after \(8\) seconds is approximately \(1.28\) meters per second.

Example 33

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 33)

A mass of \(2\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(3.50\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 2v'=-0.14v^2 \hspace{3em} v(0)=5 \]

The velocity after \(8\) seconds is approximately \(1.32\) meters per second.

Example 34

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 34)

A mass of \(6\) kg is thrown horizontally with an initial velocity of \(8\) meters per second, experiencing an initial air resistance of \(29.4\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(4\) seconds.

Answer.

The IVP is given by

\[ 6v'=-0.46v^2 \hspace{3em} v(0)=8 \]

The velocity after \(4\) seconds is approximately \(2.32\) meters per second.

Example 35

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 35)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(21.1\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=9 \]

The velocity after \(6\) seconds is approximately \(2.00\) meters per second.

Example 36

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 36)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(4\) meters per second, experiencing an initial air resistance of \(11.8\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=4 \]

The velocity after \(6\) seconds is approximately \(1.24\) meters per second.

Example 37

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 37)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(7\) meters per second, experiencing an initial air resistance of \(36.3\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(9\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=7 \]

The velocity after \(9\) seconds is approximately \(1.03\) meters per second.

Example 38

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 38)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(1.71\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=3 \]

The velocity after \(2\) seconds is approximately \(2.17\) meters per second.

Example 39

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 39)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(6.66\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(7\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=3 \]

The velocity after \(7\) seconds is approximately \(1.02\) meters per second.

Example 40

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 40)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(4\) meters per second, experiencing an initial air resistance of \(4.16\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=4 \]

The velocity after \(2\) seconds is approximately \(2.63\) meters per second.

Example 41

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 41)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(21.1\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(9\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=9 \]

The velocity after \(9\) seconds is approximately \(1.44\) meters per second.

Example 42

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 42)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(21.1\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=9 \]

The velocity after \(8\) seconds is approximately \(1.58\) meters per second.

Example 43

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 43)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(7\) meters per second, experiencing an initial air resistance of \(9.31\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(5\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=7 \]

The velocity after \(5\) seconds is approximately \(2.18\) meters per second.

Example 44

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 44)

A mass of \(2\) kg is thrown horizontally with an initial velocity of \(2\) meters per second, experiencing an initial air resistance of \(0.560\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 2v'=-0.14v^2 \hspace{3em} v(0)=2 \]

The velocity after \(2\) seconds is approximately \(1.56\) meters per second.

Example 45

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 45)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(26.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=6 \]

The velocity after \(2\) seconds is approximately \(2.84\) meters per second.

Example 46

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 46)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(8\) meters per second, experiencing an initial air resistance of \(16.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(5\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=8 \]

The velocity after \(5\) seconds is approximately \(2.22\) meters per second.

Example 47

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 47)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(4\) meters per second, experiencing an initial air resistance of \(11.8\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=4 \]

The velocity after \(2\) seconds is approximately \(2.30\) meters per second.

Example 48

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 48)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(6.84\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(7\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=6 \]

The velocity after \(7\) seconds is approximately \(1.64\) meters per second.

Example 49

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 49)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(3.15\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=3 \]

The velocity after \(3\) seconds is approximately \(1.84\) meters per second.

Example 50

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 50)

A mass of \(6\) kg is thrown horizontally with an initial velocity of \(2\) meters per second, experiencing an initial air resistance of \(1.84\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(9\) seconds.

Answer.

The IVP is given by

\[ 6v'=-0.46v^2 \hspace{3em} v(0)=2 \]

The velocity after \(9\) seconds is approximately \(0.840\) meters per second.

Example 51

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 51)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(4\) meters per second, experiencing an initial air resistance of \(4.16\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=4 \]

The velocity after \(6\) seconds is approximately \(1.56\) meters per second.

Example 52

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 52)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(21.1\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=9 \]

The velocity after \(6\) seconds is approximately \(2.00\) meters per second.

Example 53

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 53)

A mass of \(7\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(21.2\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 7v'=-0.59v^2 \hspace{3em} v(0)=6 \]

The velocity after \(8\) seconds is approximately \(1.19\) meters per second.

Example 54

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 54)

A mass of \(7\) kg is thrown horizontally with an initial velocity of \(7\) meters per second, experiencing an initial air resistance of \(28.9\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 7v'=-0.59v^2 \hspace{3em} v(0)=7 \]

The velocity after \(6\) seconds is approximately \(1.54\) meters per second.

Example 55

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 55)

A mass of \(9\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(73.7\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 9v'=-0.91v^2 \hspace{3em} v(0)=9 \]

The velocity after \(3\) seconds is approximately \(2.41\) meters per second.

Example 56

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 56)

A mass of \(6\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(4.14\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(7\) seconds.

Answer.

The IVP is given by

\[ 6v'=-0.46v^2 \hspace{3em} v(0)=3 \]

The velocity after \(7\) seconds is approximately \(1.15\) meters per second.

Example 57

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 57)

A mass of \(7\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(5.31\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 7v'=-0.59v^2 \hspace{3em} v(0)=3 \]

The velocity after \(8\) seconds is approximately \(0.992\) meters per second.

Example 58

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 58)

A mass of \(7\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(14.8\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(4\) seconds.

Answer.

The IVP is given by

\[ 7v'=-0.59v^2 \hspace{3em} v(0)=5 \]

The velocity after \(4\) seconds is approximately \(1.86\) meters per second.

Example 59

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 59)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(2\) meters per second, experiencing an initial air resistance of \(0.760\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=2 \]

The velocity after \(8\) seconds is approximately \(0.993\) meters per second.

Example 60

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 60)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(4\) meters per second, experiencing an initial air resistance of \(4.16\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=4 \]

The velocity after \(2\) seconds is approximately \(2.63\) meters per second.

Example 61

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 61)

A mass of \(2\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(11.3\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(4\) seconds.

Answer.

The IVP is given by

\[ 2v'=-0.14v^2 \hspace{3em} v(0)=9 \]

The velocity after \(4\) seconds is approximately \(2.56\) meters per second.

Example 62

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 62)

A mass of \(2\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(3.50\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(4\) seconds.

Answer.

The IVP is given by

\[ 2v'=-0.14v^2 \hspace{3em} v(0)=5 \]

The velocity after \(4\) seconds is approximately \(2.08\) meters per second.

Example 63

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 63)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(2\) meters per second, experiencing an initial air resistance of \(2.96\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(4\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=2 \]

The velocity after \(4\) seconds is approximately \(1.15\) meters per second.

Example 64

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 64)

A mass of \(9\) kg is thrown horizontally with an initial velocity of \(7\) meters per second, experiencing an initial air resistance of \(44.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 9v'=-0.91v^2 \hspace{3em} v(0)=7 \]

The velocity after \(2\) seconds is approximately \(2.90\) meters per second.

Example 65

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 65)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(4\) meters per second, experiencing an initial air resistance of \(11.8\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=4 \]

The velocity after \(6\) seconds is approximately \(1.24\) meters per second.

Example 66

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 66)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(3.15\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(9\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=3 \]

The velocity after \(9\) seconds is approximately \(1.04\) meters per second.

Example 67

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 67)

A mass of \(9\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(73.7\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 9v'=-0.91v^2 \hspace{3em} v(0)=9 \]

The velocity after \(8\) seconds is approximately \(1.09\) meters per second.

Example 68

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 68)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(8\) meters per second, experiencing an initial air resistance of \(12.2\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=8 \]

The velocity after \(8\) seconds is approximately \(1.58\) meters per second.

Example 69

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 69)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(12.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(5\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=6 \]

The velocity after \(5\) seconds is approximately \(1.94\) meters per second.

Example 70

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 70)

A mass of \(9\) kg is thrown horizontally with an initial velocity of \(4\) meters per second, experiencing an initial air resistance of \(14.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 9v'=-0.91v^2 \hspace{3em} v(0)=4 \]

The velocity after \(2\) seconds is approximately \(2.21\) meters per second.

Example 71

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 71)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(18.5\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(9\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=5 \]

The velocity after \(9\) seconds is approximately \(0.969\) meters per second.

Example 72

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 72)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(59.9\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(7\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=9 \]

The velocity after \(7\) seconds is approximately \(1.32\) meters per second.

Example 73

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 73)

A mass of \(7\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(21.2\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(5\) seconds.

Answer.

The IVP is given by

\[ 7v'=-0.59v^2 \hspace{3em} v(0)=6 \]

The velocity after \(5\) seconds is approximately \(1.70\) meters per second.

Example 74

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 74)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(7\) meters per second, experiencing an initial air resistance of \(9.31\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=7 \]

The velocity after \(6\) seconds is approximately \(1.91\) meters per second.

Example 75

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 75)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(6.50\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=5 \]

The velocity after \(8\) seconds is approximately \(1.39\) meters per second.

Example 76

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 76)

A mass of \(9\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(32.8\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 9v'=-0.91v^2 \hspace{3em} v(0)=6 \]

The velocity after \(8\) seconds is approximately \(1.03\) meters per second.

Example 77

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 77)

A mass of \(9\) kg is thrown horizontally with an initial velocity of \(8\) meters per second, experiencing an initial air resistance of \(58.2\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(9\) seconds.

Answer.

The IVP is given by

\[ 9v'=-0.91v^2 \hspace{3em} v(0)=8 \]

The velocity after \(9\) seconds is approximately \(0.966\) meters per second.

Example 78

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 78)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(15.4\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(7\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=9 \]

The velocity after \(7\) seconds is approximately \(1.80\) meters per second.

Example 79

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 79)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(4\) meters per second, experiencing an initial air resistance of \(4.16\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(4\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=4 \]

The velocity after \(4\) seconds is approximately \(1.96\) meters per second.

Example 80

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 80)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(8\) meters per second, experiencing an initial air resistance of \(47.4\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(2\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=8 \]

The velocity after \(2\) seconds is approximately \(3.23\) meters per second.

Example 81

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 81)

A mass of \(9\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(8.19\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(7\) seconds.

Answer.

The IVP is given by

\[ 9v'=-0.91v^2 \hspace{3em} v(0)=3 \]

The velocity after \(7\) seconds is approximately \(0.961\) meters per second.

Example 82

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 82)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(6.66\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=3 \]

The velocity after \(3\) seconds is approximately \(1.64\) meters per second.

Example 83

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 83)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(2\) meters per second, experiencing an initial air resistance of \(0.760\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(5\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=2 \]

The velocity after \(5\) seconds is approximately \(1.22\) meters per second.

Example 84

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 84)

A mass of \(7\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(14.8\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(7\) seconds.

Answer.

The IVP is given by

\[ 7v'=-0.59v^2 \hspace{3em} v(0)=5 \]

The velocity after \(7\) seconds is approximately \(1.27\) meters per second.

Example 85

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 85)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(6.50\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(7\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=5 \]

The velocity after \(7\) seconds is approximately \(1.53\) meters per second.

Example 86

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 86)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(2\) meters per second, experiencing an initial air resistance of \(1.04\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(4\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=2 \]

The velocity after \(4\) seconds is approximately \(1.32\) meters per second.

Example 87

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 87)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(28.3\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=9 \]

The velocity after \(8\) seconds is approximately \(1.49\) meters per second.

Example 88

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 88)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(6.66\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(4\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=3 \]

The velocity after \(4\) seconds is approximately \(1.42\) meters per second.

Example 89

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 89)

A mass of \(8\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(6.66\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(7\) seconds.

Answer.

The IVP is given by

\[ 8v'=-0.74v^2 \hspace{3em} v(0)=3 \]

The velocity after \(7\) seconds is approximately \(1.02\) meters per second.

Example 90

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 90)

A mass of \(5\) kg is thrown horizontally with an initial velocity of \(9\) meters per second, experiencing an initial air resistance of \(28.3\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 5v'=-0.35v^2 \hspace{3em} v(0)=9 \]

The velocity after \(3\) seconds is approximately \(3.11\) meters per second.

Example 91

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 91)

A mass of \(7\) kg is thrown horizontally with an initial velocity of \(2\) meters per second, experiencing an initial air resistance of \(2.36\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 7v'=-0.59v^2 \hspace{3em} v(0)=2 \]

The velocity after \(6\) seconds is approximately \(0.994\) meters per second.

Example 92

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 92)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(7\) meters per second, experiencing an initial air resistance of \(9.31\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=7 \]

The velocity after \(3\) seconds is approximately \(3.00\) meters per second.

Example 93

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 93)

A mass of \(2\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(5.04\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(7\) seconds.

Answer.

The IVP is given by

\[ 2v'=-0.14v^2 \hspace{3em} v(0)=6 \]

The velocity after \(7\) seconds is approximately \(1.52\) meters per second.

Example 94

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 94)

A mass of \(7\) kg is thrown horizontally with an initial velocity of \(3\) meters per second, experiencing an initial air resistance of \(5.31\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(6\) seconds.

Answer.

The IVP is given by

\[ 7v'=-0.59v^2 \hspace{3em} v(0)=3 \]

The velocity after \(6\) seconds is approximately \(1.19\) meters per second.

Example 95

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 95)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(8\) meters per second, experiencing an initial air resistance of \(16.6\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(8\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=8 \]

The velocity after \(8\) seconds is approximately \(1.55\) meters per second.

Example 96

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 96)

A mass of \(7\) kg is thrown horizontally with an initial velocity of \(7\) meters per second, experiencing an initial air resistance of \(28.9\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(5\) seconds.

Answer.

The IVP is given by

\[ 7v'=-0.59v^2 \hspace{3em} v(0)=7 \]

The velocity after \(5\) seconds is approximately \(1.77\) meters per second.

Example 97

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 97)

A mass of \(2\) kg is thrown horizontally with an initial velocity of \(5\) meters per second, experiencing an initial air resistance of \(3.50\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(9\) seconds.

Answer.

The IVP is given by

\[ 2v'=-0.14v^2 \hspace{3em} v(0)=5 \]

The velocity after \(9\) seconds is approximately \(1.20\) meters per second.

Example 98

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 98)

A mass of \(3\) kg is thrown horizontally with an initial velocity of \(2\) meters per second, experiencing an initial air resistance of \(0.760\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(4\) seconds.

Answer.

The IVP is given by

\[ 3v'=-0.19v^2 \hspace{3em} v(0)=2 \]

The velocity after \(4\) seconds is approximately \(1.33\) meters per second.

Example 99

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 99)

A mass of \(2\) kg is thrown horizontally with an initial velocity of \(4\) meters per second, experiencing an initial air resistance of \(2.24\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(5\) seconds.

Answer.

The IVP is given by

\[ 2v'=-0.14v^2 \hspace{3em} v(0)=4 \]

The velocity after \(5\) seconds is approximately \(1.67\) meters per second.

Example 100

F3m - Motion with quadratic drag. Model and analyze the horizontal motion of an object with quadratic drag. (ver. 100)

A mass of \(4\) kg is thrown horizontally with an initial velocity of \(6\) meters per second, experiencing an initial air resistance of \(9.36\) Newtons. Assume that acceleration due to gravity is roughly 9.81 \(\textrm{m}/\textrm{s}^2\).

Write an initial value problem (IVP) modeling the horizontal velocity of this mass. Then solve this IVP to compute the mass's horizontal velocity after \(3\) seconds.

Answer.

The IVP is given by

\[ 4v'=-0.26v^2 \hspace{3em} v(0)=6 \]

The velocity after \(3\) seconds is approximately \(2.76\) meters per second.