Chapter D1.3, Problem 46E

(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 given 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).