Chapter 12, Problem 67RE

(a)

To determine

To find: The height to which the ball bounces after it strikes the ground the third time..

Answer to Problem 67RE

The required height is $\frac{135}{16}\text{ft}$ .

Explanation of Solution

The height after the ball strikes the third time is calculated as,

  $\begin{array}{l}h={\left(\frac{3}{4}\right)}^3\left(20\right)\\ =\frac{135}{16}\text{ft}\end{array}$

Therefore, the required height is $\frac{135}{16}\text{ft}$ .

(b)

To determine

To find: The height to which the ball bounces after it strikes the ground the $n^{\text{th}}$ time.

Answer to Problem 67RE

The required height is $h={\left(\frac{3}{4}\right)}^n\left(20\right)$ .

Explanation of Solution

The height after the ball strikes the $n^{\text{th}}$ time is calculated as,

  $h={\left(\frac{3}{4}\right)}^n\left(20\right)$

Therefore, the required height is $h={\left(\frac{3}{4}\right)}^n\left(20\right)$ .

(c)

To determine

To find: The number of times the ball bounces so it reaches the height $6\text{inches}$ .

Answer to Problem 67RE

The ball must bounce $\text{13}\text{times}$ .

Explanation of Solution

The number of times the ball bounces is calculated as,

  $\begin{array}{c}0.6={\left(\frac{3}{4}\right)}^n\left(20\right)\\ n=12.82\\ \approx 13\text{times}\end{array}$

Therefore, the ball must bounce $\text{13}\text{times}$ .

(d)

To determine

To find: The total distance balls travelled before ball stops bouncing.

Answer to Problem 67RE

The total distance travelled when the ball stops is $80\text{ft}$ .

Explanation of Solution

The total distance travelled is calculated as,

  $\begin{array}{c}T=\frac{20}{1-\frac{3}{4}}\\ =\frac{20\left(4\right)}{1}\\ =80\text{ft}\end{array}$

Therefore, the total distance travelled when the ball stops is $80\text{ft}$ .