## 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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)

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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)

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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)

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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)

#### 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)

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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)

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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 \(\textrm{m}/\textrm{s}^2\).

#### 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.