Chapter 2.3, Problem 28P

(a)

To determine

The velocity $v(t)$ of the body at any time. Where a body of mass $m$ is projected vertically upward with initial velocity $v_0$ in a medium offering a resistance $k\left|v\right|$, where $k$ is constant.

(b)

To determine

To calculate:

The limit of $v(t)$ as $k\to 0$ by using $v(t)=-\frac{mg}{k}+\left(v_0+\frac{mg}{k}\right)e^{-kt/m}$. Effect on the velocity of a mass $m$ projected upward with initial velocity $v_0$ in a vacuum.

(c)

To determine

To calculate:

The limit of $v(t)$ as $m\to 0$ by using $v(t)=-\frac{mg}{k}+\left(v_0+\frac{mg}{k}\right)e^{-kt/m}$