Chapter 9.3, Problem 48E

a.

To determine

To show: The equation $m\cdot v^{\prime }\left(t\right)=mg+f\left(v\right)$ can be written in the form $v\text{'}\left(t\right)=g-bv$ where $b=\frac{R}{m}$.

b.

To determine

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

c.

To determine

To find: The solution of the separable equation.

d.

To determine

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