## C3m - Model and analyze the vertical motion of an object with linear drag

#### Example 1

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 1)

A water droplet with a radius of \(0.000312\) meters has a mass of about \(9.59 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.845\) meters per second.

Write an initial value problem (IVP) modeling the velocity of this water droplet when dropped from rest, assuming that the acceleration due to gravity is roughly \(9.81\hspace{0.3em}\mathrm{m}/\mathrm{s}^2\). Then solve this IVP to compute the droplet's velocity after \(0.03\) seconds.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 11.6\).The velocity after \(0.03\) seconds is approximately \(-0.249\) meters per second.

#### Example 2

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 2)

A water droplet with a radius of \(0.000416\) meters has a mass of about \(2.26 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.975\) meters per second.

Write an initial value problem (IVP) modeling the velocity of this water droplet when dropped from rest, assuming that the acceleration due to gravity is roughly \(9.81\hspace{0.3em}\mathrm{m}/\mathrm{s}^2\). Then solve this IVP to compute the droplet's velocity after \(0.03\) seconds.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 10.1\).The velocity after \(0.03\) seconds is approximately \(-0.254\) meters per second.

#### Example 3

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 3)

A water droplet with a radius of \(0.000104\) meters has a mass of about \(3.51 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.487\) meters per second.

Write an initial value problem (IVP) modeling the velocity of this water droplet when dropped from rest, assuming that the acceleration due to gravity is roughly \(9.81\hspace{0.3em}\mathrm{m}/\mathrm{s}^2\). Then solve this IVP to compute the droplet's velocity after \(0.04\) seconds.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 20.1\).The velocity after \(0.04\) seconds is approximately \(-0.269\) meters per second.

#### Example 4

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 4)

A water droplet with a radius of \(0.000183\) meters has a mass of about \(1.93 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.647\) meters per second.

Write an initial value problem (IVP) modeling the velocity of this water droplet when dropped from rest, assuming that the acceleration due to gravity is roughly \(9.81\hspace{0.3em}\mathrm{m}/\mathrm{s}^2\). Then solve this IVP to compute the droplet's velocity after \(0.02\) seconds.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 15.2\).The velocity after \(0.02\) seconds is approximately \(-0.169\) meters per second.

#### Example 5

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 5)

A water droplet with a radius of \(5.59 \times 10^{-6}\) meters has a mass of about \(5.48 \times 10^{-14}\) kilograms and a downward terminal velocity of approximately \(0.113\) meters per second.

Write an initial value problem (IVP) modeling the velocity of this water droplet when dropped from rest, assuming that the acceleration due to gravity is roughly \(9.81\hspace{0.3em}\mathrm{m}/\mathrm{s}^2\). Then solve this IVP to compute the droplet's velocity after \(0.03\) seconds.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 86.8\).The velocity after \(0.03\) seconds is approximately \(-0.105\) meters per second.

#### Example 6

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 6)

A water droplet with a radius of \(0.000354\) meters has a mass of about \(1.39 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.899\) meters per second.

Write an initial value problem (IVP) modeling the velocity of this water droplet when dropped from rest, assuming that the acceleration due to gravity is roughly \(9.81\hspace{0.3em}\mathrm{m}/\mathrm{s}^2\). Then solve this IVP to compute the droplet's velocity after \(0.04\) seconds.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 10.9\).The velocity after \(0.04\) seconds is approximately \(-0.318\) meters per second.

#### Example 7

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 7)

A water droplet with a radius of \(0.000307\) meters has a mass of about \(9.12 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.838\) meters per second.

Write an initial value problem (IVP) modeling the velocity of this water droplet when dropped from rest, assuming that the acceleration due to gravity is roughly \(9.81\hspace{0.3em}\mathrm{m}/\mathrm{s}^2\). Then solve this IVP to compute the droplet's velocity after \(0.04\) seconds.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 11.7\).The velocity after \(0.04\) seconds is approximately \(-0.313\) meters per second.

#### Example 8

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 8)

A water droplet with a radius of \(0.000342\) meters has a mass of about \(1.26 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.884\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 11.1\).The velocity after \(0.04\) seconds is approximately \(-0.317\) meters per second.

#### Example 9

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 9)

A water droplet with a radius of \(0.000180\) meters has a mass of about \(1.84 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.642\) meters per second.

Write an initial value problem (IVP) modeling the velocity of this water droplet when dropped from rest, assuming that the acceleration due to gravity is roughly \(9.81\hspace{0.3em}\mathrm{m}/\mathrm{s}^2\). Then solve this IVP to compute the droplet's velocity after \(0.02\) seconds.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 15.3\).The velocity after \(0.02\) seconds is approximately \(-0.169\) meters per second.

#### Example 10

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 10)

A water droplet with a radius of \(0.000407\) meters has a mass of about \(2.11 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.964\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 10.2\).The velocity after \(0.03\) seconds is approximately \(-0.254\) meters per second.

#### Example 11

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 11)

A water droplet with a radius of \(0.000127\) meters has a mass of about \(6.39 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.538\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 18.2\).The velocity after \(0.03\) seconds is approximately \(-0.227\) meters per second.

#### Example 12

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 12)

A water droplet with a radius of \(0.000127\) meters has a mass of about \(6.46 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.539\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 18.2\).The velocity after \(0.03\) seconds is approximately \(-0.227\) meters per second.

#### Example 13

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 13)

A water droplet with a radius of \(0.0000421\) meters has a mass of about \(2.34 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.310\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 31.6\).The velocity after \(0.04\) seconds is approximately \(-0.223\) meters per second.

#### Example 14

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 14)

A water droplet with a radius of \(7.51 \times 10^{-6}\) meters has a mass of about \(1.33 \times 10^{-13}\) kilograms and a downward terminal velocity of approximately \(0.131\) meters per second.

Write an initial value problem (IVP) modeling the velocity of this water droplet when dropped from rest, assuming that the acceleration due to gravity is roughly \(9.81\hspace{0.3em}\mathrm{m}/\mathrm{s}^2\). Then solve this IVP to compute the droplet's velocity after \(0.02\) seconds.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 74.9\).The velocity after \(0.02\) seconds is approximately \(-0.102\) meters per second.

#### Example 15

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 15)

A water droplet with a radius of \(0.000218\) meters has a mass of about \(3.26 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.706\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 13.9\).The velocity after \(0.04\) seconds is approximately \(-0.301\) meters per second.

#### Example 16

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 16)

A water droplet with a radius of \(0.0000987\) meters has a mass of about \(3.02 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.475\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 20.7\).The velocity after \(0.03\) seconds is approximately \(-0.219\) meters per second.

#### Example 17

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 17)

A water droplet with a radius of \(0.000112\) meters has a mass of about \(4.42 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.506\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 19.4\).The velocity after \(0.03\) seconds is approximately \(-0.223\) meters per second.

#### Example 18

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 18)

A water droplet with a radius of \(0.000410\) meters has a mass of about \(2.17 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.968\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 10.1\).The velocity after \(0.03\) seconds is approximately \(-0.254\) meters per second.

#### Example 19

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 19)

A water droplet with a radius of \(0.0000871\) meters has a mass of about \(2.07 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.446\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 22.0\).The velocity after \(0.04\) seconds is approximately \(-0.261\) meters per second.

#### Example 20

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 20)

A water droplet with a radius of \(0.0000979\) meters has a mass of about \(2.95 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.473\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 20.7\).The velocity after \(0.03\) seconds is approximately \(-0.219\) meters per second.

#### Example 21

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 21)

A water droplet with a radius of \(0.0000454\) meters has a mass of about \(2.94 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.322\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 30.5\).The velocity after \(0.02\) seconds is approximately \(-0.147\) meters per second.

#### Example 22

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 22)

A water droplet with a radius of \(0.0000471\) meters has a mass of about \(3.28 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.328\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 29.9\).The velocity after \(0.03\) seconds is approximately \(-0.194\) meters per second.

#### Example 23

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 23)

A water droplet with a radius of \(0.0000158\) meters has a mass of about \(1.24 \times 10^{-12}\) kilograms and a downward terminal velocity of approximately \(0.190\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 51.6\).The velocity after \(0.02\) seconds is approximately \(-0.122\) meters per second.

#### Example 24

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 24)

A water droplet with a radius of \(0.0000971\) meters has a mass of about \(2.87 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.471\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 20.8\).The velocity after \(0.04\) seconds is approximately \(-0.266\) meters per second.

#### Example 25

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 25)

A water droplet with a radius of \(0.000126\) meters has a mass of about \(6.24 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.536\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 18.3\).The velocity after \(0.04\) seconds is approximately \(-0.278\) meters per second.

#### Example 26

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 26)

A water droplet with a radius of \(0.000364\) meters has a mass of about \(1.52 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.912\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 10.8\).The velocity after \(0.04\) seconds is approximately \(-0.319\) meters per second.

#### Example 27

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 27)

A water droplet with a radius of \(0.0000254\) meters has a mass of about \(5.16 \times 10^{-12}\) kilograms and a downward terminal velocity of approximately \(0.241\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 40.7\).The velocity after \(0.04\) seconds is approximately \(-0.194\) meters per second.

#### Example 28

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 28)

A water droplet with a radius of \(0.000106\) meters has a mass of about \(3.73 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.492\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 19.9\).The velocity after \(0.04\) seconds is approximately \(-0.270\) meters per second.

#### Example 29

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 29)

A water droplet with a radius of \(0.000304\) meters has a mass of about \(8.80 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.833\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 11.8\).The velocity after \(0.03\) seconds is approximately \(-0.248\) meters per second.

#### Example 30

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 30)

A water droplet with a radius of \(0.0000787\) meters has a mass of about \(1.53 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.424\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 23.1\).The velocity after \(0.04\) seconds is approximately \(-0.256\) meters per second.

#### Example 31

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 31)

A water droplet with a radius of \(4.83 \times 10^{-6}\) meters has a mass of about \(3.53 \times 10^{-14}\) kilograms and a downward terminal velocity of approximately \(0.105\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 93.4\).The velocity after \(0.03\) seconds is approximately \(-0.0986\) meters per second.

#### Example 32

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 32)

A water droplet with a radius of \(0.000141\) meters has a mass of about \(8.84 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.568\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 17.3\).The velocity after \(0.03\) seconds is approximately \(-0.230\) meters per second.

#### Example 33

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 33)

A water droplet with a radius of \(8.46 \times 10^{-6}\) meters has a mass of about \(1.90 \times 10^{-13}\) kilograms and a downward terminal velocity of approximately \(0.139\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 70.6\).The velocity after \(0.03\) seconds is approximately \(-0.122\) meters per second.

#### Example 34

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 34)

A water droplet with a radius of \(0.000189\) meters has a mass of about \(2.12 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.657\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 14.9\).The velocity after \(0.04\) seconds is approximately \(-0.295\) meters per second.

#### Example 35

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 35)

A water droplet with a radius of \(0.0000479\) meters has a mass of about \(3.46 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.331\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 29.6\).The velocity after \(0.04\) seconds is approximately \(-0.230\) meters per second.

#### Example 36

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 36)

A water droplet with a radius of \(0.000324\) meters has a mass of about \(1.07 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.861\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 11.4\).The velocity after \(0.03\) seconds is approximately \(-0.249\) meters per second.

#### Example 37

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 37)

A water droplet with a radius of \(0.000275\) meters has a mass of about \(6.50 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.792\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 12.4\).The velocity after \(0.04\) seconds is approximately \(-0.309\) meters per second.

#### Example 38

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 38)

A water droplet with a radius of \(0.0000381\) meters has a mass of about \(1.74 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.295\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 33.3\).The velocity after \(0.02\) seconds is approximately \(-0.143\) meters per second.

#### Example 39

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 39)

A water droplet with a radius of \(0.000294\) meters has a mass of about \(7.95 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.819\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 12.0\).The velocity after \(0.02\) seconds is approximately \(-0.174\) meters per second.

#### Example 40

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 40)

A water droplet with a radius of \(0.0000813\) meters has a mass of about \(1.69 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.431\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 22.8\).The velocity after \(0.03\) seconds is approximately \(-0.213\) meters per second.

#### Example 41

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 41)

A water droplet with a radius of \(0.0000666\) meters has a mass of about \(9.27 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.390\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 25.2\).The velocity after \(0.04\) seconds is approximately \(-0.247\) meters per second.

#### Example 42

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 42)

A water droplet with a radius of \(0.0000809\) meters has a mass of about \(1.66 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.430\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 22.8\).The velocity after \(0.04\) seconds is approximately \(-0.257\) meters per second.

#### Example 43

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 43)

A water droplet with a radius of \(0.0000386\) meters has a mass of about \(1.81 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.297\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 33.0\).The velocity after \(0.04\) seconds is approximately \(-0.218\) meters per second.

#### Example 44

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 44)

A water droplet with a radius of \(8.70 \times 10^{-6}\) meters has a mass of about \(2.07 \times 10^{-13}\) kilograms and a downward terminal velocity of approximately \(0.141\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 69.6\).The velocity after \(0.02\) seconds is approximately \(-0.106\) meters per second.

#### Example 45

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 45)

A water droplet with a radius of \(0.000316\) meters has a mass of about \(9.93 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.850\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 11.5\).The velocity after \(0.03\) seconds is approximately \(-0.249\) meters per second.

#### Example 46

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 46)

A water droplet with a radius of \(0.0000743\) meters has a mass of about \(1.29 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.412\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 23.8\).The velocity after \(0.04\) seconds is approximately \(-0.253\) meters per second.

#### Example 47

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 47)

A water droplet with a radius of \(0.000325\) meters has a mass of about \(1.08 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.862\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 11.4\).The velocity after \(0.03\) seconds is approximately \(-0.249\) meters per second.

#### Example 48

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 48)

A water droplet with a radius of \(0.0000267\) meters has a mass of about \(5.98 \times 10^{-12}\) kilograms and a downward terminal velocity of approximately \(0.247\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 39.7\).The velocity after \(0.03\) seconds is approximately \(-0.172\) meters per second.

#### Example 49

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 49)

A water droplet with a radius of \(0.000129\) meters has a mass of about \(6.68 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.542\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 18.1\).The velocity after \(0.02\) seconds is approximately \(-0.165\) meters per second.

#### Example 50

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 50)

A water droplet with a radius of \(0.000160\) meters has a mass of about \(1.28 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.604\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 16.2\).The velocity after \(0.02\) seconds is approximately \(-0.168\) meters per second.

#### Example 51

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 51)

A water droplet with a radius of \(0.0000482\) meters has a mass of about \(3.53 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.332\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 29.5\).The velocity after \(0.02\) seconds is approximately \(-0.148\) meters per second.

#### Example 52

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 52)

A water droplet with a radius of \(0.0000721\) meters has a mass of about \(1.18 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.406\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 24.2\).The velocity after \(0.04\) seconds is approximately \(-0.252\) meters per second.

#### Example 53

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 53)

A water droplet with a radius of \(0.000253\) meters has a mass of about \(5.07 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.760\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 12.9\).The velocity after \(0.03\) seconds is approximately \(-0.244\) meters per second.

#### Example 54

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 54)

A water droplet with a radius of \(0.000224\) meters has a mass of about \(3.52 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.715\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 13.7\).The velocity after \(0.03\) seconds is approximately \(-0.241\) meters per second.

#### Example 55

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 55)

A water droplet with a radius of \(0.000417\) meters has a mass of about \(2.28 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.976\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 10.1\).The velocity after \(0.04\) seconds is approximately \(-0.323\) meters per second.

#### Example 56

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 56)

A water droplet with a radius of \(0.000175\) meters has a mass of about \(1.69 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.633\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 15.5\).The velocity after \(0.02\) seconds is approximately \(-0.169\) meters per second.

#### Example 57

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 57)

A water droplet with a radius of \(0.000236\) meters has a mass of about \(4.12 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.734\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 13.4\).The velocity after \(0.02\) seconds is approximately \(-0.172\) meters per second.

#### Example 58

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 58)

A water droplet with a radius of \(0.000211\) meters has a mass of about \(2.94 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.694\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 14.1\).The velocity after \(0.03\) seconds is approximately \(-0.240\) meters per second.

#### Example 59

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 59)

A water droplet with a radius of \(0.0000351\) meters has a mass of about \(1.35 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.283\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 34.7\).The velocity after \(0.02\) seconds is approximately \(-0.142\) meters per second.

#### Example 60

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 60)

A water droplet with a radius of \(0.0000471\) meters has a mass of about \(3.28 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.328\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 29.9\).The velocity after \(0.03\) seconds is approximately \(-0.194\) meters per second.

#### Example 61

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 61)

A water droplet with a radius of \(0.0000161\) meters has a mass of about \(1.32 \times 10^{-12}\) kilograms and a downward terminal velocity of approximately \(0.192\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 51.1\).The velocity after \(0.04\) seconds is approximately \(-0.167\) meters per second.

#### Example 62

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 62)

A water droplet with a radius of \(9.20 \times 10^{-6}\) meters has a mass of about \(2.45 \times 10^{-13}\) kilograms and a downward terminal velocity of approximately \(0.145\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 67.7\).The velocity after \(0.03\) seconds is approximately \(-0.126\) meters per second.

#### Example 63

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 63)

A water droplet with a radius of \(0.000317\) meters has a mass of about \(1.00 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.851\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 11.5\).The velocity after \(0.02\) seconds is approximately \(-0.175\) meters per second.

#### Example 64

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 64)

A water droplet with a radius of \(0.000393\) meters has a mass of about \(1.91 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.948\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 10.3\).The velocity after \(0.04\) seconds is approximately \(-0.321\) meters per second.

#### Example 65

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 65)

A water droplet with a radius of \(0.000278\) meters has a mass of about \(6.75 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.797\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 12.3\).The velocity after \(0.02\) seconds is approximately \(-0.174\) meters per second.

#### Example 66

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 66)

A water droplet with a radius of \(0.000110\) meters has a mass of about \(4.21 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.502\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 19.5\).The velocity after \(0.02\) seconds is approximately \(-0.162\) meters per second.

#### Example 67

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 67)

A water droplet with a radius of \(0.000389\) meters has a mass of about \(1.85 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.943\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 10.4\).The velocity after \(0.04\) seconds is approximately \(-0.321\) meters per second.

#### Example 68

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 68)

A water droplet with a radius of \(0.0000256\) meters has a mass of about \(5.29 \times 10^{-12}\) kilograms and a downward terminal velocity of approximately \(0.242\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 40.5\).The velocity after \(0.04\) seconds is approximately \(-0.194\) meters per second.

#### Example 69

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 69)

A water droplet with a radius of \(0.000110\) meters has a mass of about \(4.21 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.502\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 19.5\).The velocity after \(0.03\) seconds is approximately \(-0.223\) meters per second.

#### Example 70

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 70)

A water droplet with a radius of \(0.000366\) meters has a mass of about \(1.55 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.915\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 10.7\).The velocity after \(0.03\) seconds is approximately \(-0.252\) meters per second.

#### Example 71

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 71)

A water droplet with a radius of \(0.000296\) meters has a mass of about \(8.18 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.823\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 11.9\).The velocity after \(0.03\) seconds is approximately \(-0.247\) meters per second.

#### Example 72

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 72)

A water droplet with a radius of \(0.000288\) meters has a mass of about \(7.49 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.811\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 12.1\).The velocity after \(0.04\) seconds is approximately \(-0.311\) meters per second.

#### Example 73

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 73)

A water droplet with a radius of \(0.000226\) meters has a mass of about \(3.64 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.719\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 13.6\).The velocity after \(0.03\) seconds is approximately \(-0.242\) meters per second.

#### Example 74

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 74)

A water droplet with a radius of \(0.0000423\) meters has a mass of about \(2.38 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.311\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 31.5\).The velocity after \(0.03\) seconds is approximately \(-0.190\) meters per second.

#### Example 75

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 75)

A water droplet with a radius of \(0.0000750\) meters has a mass of about \(1.33 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.414\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 23.7\).The velocity after \(0.03\) seconds is approximately \(-0.211\) meters per second.

#### Example 76

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 76)

A water droplet with a radius of \(0.000370\) meters has a mass of about \(1.59 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.919\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 10.7\).The velocity after \(0.03\) seconds is approximately \(-0.252\) meters per second.

#### Example 77

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 77)

A water droplet with a radius of \(0.000383\) meters has a mass of about \(1.77 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.936\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 10.5\).The velocity after \(0.04\) seconds is approximately \(-0.321\) meters per second.

#### Example 78

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 78)

A water droplet with a radius of \(0.0000397\) meters has a mass of about \(1.96 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.301\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 32.6\).The velocity after \(0.04\) seconds is approximately \(-0.219\) meters per second.

#### Example 79

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 79)

A water droplet with a radius of \(0.0000589\) meters has a mass of about \(6.43 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.367\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 26.7\).The velocity after \(0.02\) seconds is approximately \(-0.152\) meters per second.

#### Example 80

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 80)

A water droplet with a radius of \(0.000281\) meters has a mass of about \(7.01 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.802\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 12.2\).The velocity after \(0.04\) seconds is approximately \(-0.310\) meters per second.

#### Example 81

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 81)

A water droplet with a radius of \(0.000348\) meters has a mass of about \(1.33 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.892\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 11.0\).The velocity after \(0.02\) seconds is approximately \(-0.176\) meters per second.

#### Example 82

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 82)

A water droplet with a radius of \(0.000302\) meters has a mass of about \(8.67 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.831\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 11.8\).The velocity after \(0.02\) seconds is approximately \(-0.175\) meters per second.

#### Example 83

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 83)

A water droplet with a radius of \(0.0000248\) meters has a mass of about \(4.79 \times 10^{-12}\) kilograms and a downward terminal velocity of approximately \(0.238\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 41.2\).The velocity after \(0.02\) seconds is approximately \(-0.134\) meters per second.

#### Example 84

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 84)

A water droplet with a radius of \(0.000224\) meters has a mass of about \(3.55 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.716\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 13.7\).The velocity after \(0.03\) seconds is approximately \(-0.241\) meters per second.

#### Example 85

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 85)

A water droplet with a radius of \(0.0000821\) meters has a mass of about \(1.74 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.433\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 22.7\).The velocity after \(0.03\) seconds is approximately \(-0.214\) meters per second.

#### Example 86

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 86)

A water droplet with a radius of \(0.0000477\) meters has a mass of about \(3.40 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.330\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 29.7\).The velocity after \(0.02\) seconds is approximately \(-0.148\) meters per second.

#### Example 87

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 87)

A water droplet with a radius of \(0.000112\) meters has a mass of about \(4.37 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.505\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 19.4\).The velocity after \(0.04\) seconds is approximately \(-0.273\) meters per second.

#### Example 88

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 88)

A water droplet with a radius of \(0.000268\) meters has a mass of about \(6.02 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.782\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 12.5\).The velocity after \(0.02\) seconds is approximately \(-0.174\) meters per second.

#### Example 89

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 89)

A water droplet with a radius of \(0.000339\) meters has a mass of about \(1.22 \times 10^{-8}\) kilograms and a downward terminal velocity of approximately \(0.880\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 11.1\).The velocity after \(0.02\) seconds is approximately \(-0.176\) meters per second.

#### Example 90

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 90)

A water droplet with a radius of \(0.000105\) meters has a mass of about \(3.60 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.489\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 20.1\).The velocity after \(0.04\) seconds is approximately \(-0.270\) meters per second.

#### Example 91

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 91)

A water droplet with a radius of \(0.000224\) meters has a mass of about \(3.55 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.716\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 13.7\).The velocity after \(0.02\) seconds is approximately \(-0.172\) meters per second.

#### Example 92

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 92)

A water droplet with a radius of \(0.0000329\) meters has a mass of about \(1.11 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.274\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 35.8\).The velocity after \(0.04\) seconds is approximately \(-0.209\) meters per second.

#### Example 93

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 93)

A water droplet with a radius of \(0.0000145\) meters has a mass of about \(9.57 \times 10^{-13}\) kilograms and a downward terminal velocity of approximately \(0.182\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 53.9\).The velocity after \(0.03\) seconds is approximately \(-0.146\) meters per second.

#### Example 94

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 94)

A water droplet with a radius of \(0.000250\) meters has a mass of about \(4.92 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.756\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 13.0\).The velocity after \(0.02\) seconds is approximately \(-0.173\) meters per second.

#### Example 95

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 95)

A water droplet with a radius of \(0.0000471\) meters has a mass of about \(3.28 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.328\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 29.9\).The velocity after \(0.04\) seconds is approximately \(-0.229\) meters per second.

#### Example 96

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 96)

A water droplet with a radius of \(0.000237\) meters has a mass of about \(4.19 \times 10^{-9}\) kilograms and a downward terminal velocity of approximately \(0.736\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 13.3\).The velocity after \(0.04\) seconds is approximately \(-0.304\) meters per second.

#### Example 97

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 97)

A water droplet with a radius of \(0.0000191\) meters has a mass of about \(2.19 \times 10^{-12}\) kilograms and a downward terminal velocity of approximately \(0.209\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 46.9\).The velocity after \(0.03\) seconds is approximately \(-0.158\) meters per second.

#### Example 98

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 98)

A water droplet with a radius of \(0.0000434\) meters has a mass of about \(2.57 \times 10^{-11}\) kilograms and a downward terminal velocity of approximately \(0.315\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 31.1\).The velocity after \(0.02\) seconds is approximately \(-0.146\) meters per second.

#### Example 99

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 99)

A water droplet with a radius of \(0.0000101\) meters has a mass of about \(3.25 \times 10^{-13}\) kilograms and a downward terminal velocity of approximately \(0.152\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 64.5\).The velocity after \(0.03\) seconds is approximately \(-0.130\) meters per second.

#### Example 100

## C3m - Model and analyze the vertical motion of an object with linear drag (ver. 100)

A water droplet with a radius of \(0.0000761\) meters has a mass of about \(1.38 \times 10^{-10}\) kilograms and a downward terminal velocity of approximately \(0.417\) meters per second.

#### Answer.

The IVP is given by

\[v'+Av=-g \hspace{3em} v(0)=0\]

where \(g=9.81\) and \(A\approx 23.5\).The velocity after \(0.03\) seconds is approximately \(-0.211\) meters per second.