Chapter 11.6, Problem 7P

To determine

To calculate:

Total vertical distance traveled by the ball before its stops launching.

Answer to Problem 7P

Total vertical distance traveled by the ball before its stops launching is $480m$ .

Explanation of Solution

Give information:

First distance up and down is $d=24m$

The rebound factor is $e=0.95$

Calculation:

Total distance is,

  $=24+24\left(0.95\right)+24{\left(0.95\right)}^2+\mathrm{...}$

This is an infinite geometric series

Where,

  $a=24$

  $r=0.95$

Sum of all terms are,

  $\begin{array}{l}S=\frac{a}{\left(1-r\right)}\\ S=\frac{24}{\left(1-0.95\right)}\\ S=\frac{24}{0.05}\\ S=480m\end{array}$

Therefore, Total vertical distance traveled by the ball before its stops launching is $480m$ .