Chapter 2.3, Problem 25P

(a)

To determine

The height $x_m$ attained by the body which is the maximum and the time $t_m$ at which the maximum height is reached.

(b)

To determine

To show: The functions can be expressed as $t_m=\frac{v_0}{g}\left[1-\frac{1}{2}\frac{k{v}_0}{mg}+\frac{1}{3}{\left(\frac{k{v}_0}{mg}\right)}^2-\mathrm{...}\right]$ and $x_m=\frac{v^2{}_0}{2g}\left[1-\frac{2}{3}\frac{k{v}_0}{mg}+\frac{1}{2}{\left(\frac{k{v}_0}{mg}\right)}^2-\mathrm{...}\right]$  for $\frac{k{v}_0}{mg}<1$.

(c)

To determine

To show:  The quantity $\frac{k{v}_0}{mg}$ has no dimension.