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


Example 1

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

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

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

Answer.

The IVP is given by

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

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


Example 2

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

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

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

Answer.

The IVP is given by

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

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


Example 3

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

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

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

Answer.

The IVP is given by

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

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


Example 4

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

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

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

Answer.

The IVP is given by

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

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


Example 5

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

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

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

Answer.

The IVP is given by

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

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


Example 6

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

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

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

Answer.

The IVP is given by

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

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


Example 7

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

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

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

Answer.

The IVP is given by

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

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


Example 8

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

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

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

Answer.

The IVP is given by

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

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


Example 9

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

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

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

Answer.

The IVP is given by

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

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


Example 10

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

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

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

Answer.

The IVP is given by

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

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


Example 11

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

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

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

Answer.

The IVP is given by

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

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


Example 12

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

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

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

Answer.

The IVP is given by

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

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


Example 13

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

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

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

Answer.

The IVP is given by

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

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


Example 14

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

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

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

Answer.

The IVP is given by

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

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


Example 15

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

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

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

Answer.

The IVP is given by

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

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


Example 16

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

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

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

Answer.

The IVP is given by

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

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


Example 17

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

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

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

Answer.

The IVP is given by

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

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


Example 18

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

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

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

Answer.

The IVP is given by

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

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


Example 19

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

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

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

Answer.

The IVP is given by

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

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


Example 20

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

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

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

Answer.

The IVP is given by

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

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


Example 21

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

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

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

Answer.

The IVP is given by

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

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


Example 22

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

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

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

Answer.

The IVP is given by

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

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


Example 23

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

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

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

Answer.

The IVP is given by

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

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


Example 24

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

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

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

Answer.

The IVP is given by

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

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


Example 25

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

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

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

Answer.

The IVP is given by

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

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


Example 26

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

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

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

Answer.

The IVP is given by

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

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


Example 27

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

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

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

Answer.

The IVP is given by

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

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


Example 28

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

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

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

Answer.

The IVP is given by

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

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


Example 29

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

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

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

Answer.

The IVP is given by

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

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


Example 30

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

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

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

Answer.

The IVP is given by

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

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


Example 31

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

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

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

Answer.

The IVP is given by

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

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


Example 32

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

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

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

Answer.

The IVP is given by

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

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


Example 33

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

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

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

Answer.

The IVP is given by

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

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


Example 34

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

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

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

Answer.

The IVP is given by

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

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


Example 35

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

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

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

Answer.

The IVP is given by

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

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


Example 36

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

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

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

Answer.

The IVP is given by

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

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


Example 37

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

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

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

Answer.

The IVP is given by

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

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


Example 38

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

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

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

Answer.

The IVP is given by

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

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


Example 39

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

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

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

Answer.

The IVP is given by

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

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


Example 40

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

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

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

Answer.

The IVP is given by

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

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


Example 41

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

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

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

Answer.

The IVP is given by

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

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


Example 42

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

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

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

Answer.

The IVP is given by

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

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


Example 43

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

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

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

Answer.

The IVP is given by

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

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


Example 44

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

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

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

Answer.

The IVP is given by

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

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


Example 45

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

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

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

Answer.

The IVP is given by

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

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


Example 46

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

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

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

Answer.

The IVP is given by

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

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


Example 47

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

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

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

Answer.

The IVP is given by

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

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


Example 48

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

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

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

Answer.

The IVP is given by

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

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


Example 49

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

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

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

Answer.

The IVP is given by

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

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


Example 50

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

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

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

Answer.

The IVP is given by

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

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