Chapter 9.3, Problem 47E

(a)

To determine

To show: The differential equation $m\cdot v^{\prime }\left(t\right)=mg+f\left(v\right)$ can be written in the form $v^{\prime }\left(t\right)=g-a{v}^2$.

(b)

To determine

To find: The positive value the $v$ such that $v^{\prime }\left(t\right)=0$.

(c)

To determine

To find: The solution of the given separable equation $v^{\prime }\left(t\right)=g-a{v}^2$ by assuming $v\left(0\right)=0$ and $0<v^2<\frac{g}{a}$.

(d)

To determine

To sketch: The graph for the solution obtained in part (c) and to verify the terminal velocity obtained in part (b).