Chapter 7.9, Problem 63E

a.

To determine

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

b.

To determine

To find: The terminal velocity, that is the value of v such that $v\text{'}\left(t\right)=0$.

c.

To determine

To find: The solution of the given separable equation with initial value $v\left(0\right)=0$ and $0<v<\frac{g}{b}$.

d.

To determine

To verify: The terminal velocity satisfies with the value in part (b) and also graph the given function for $g=9.8{\text{m/s}}^{\text{2}}$, $m=1$ kg and $R=0.1$ kg/m.