Chapter 11.4, Problem 53PPS

To determine

Find the total vertical distance the ball will travel if it is dropped from an elevation of 30 feet.

Answer to Problem 53PPS

The total vertical distance is 600 feet.

Explanation of Solution

Given:

If a rubber ball can bounce back to 95%of its original height, what is the total vertical distance that it will travel if it is dropped from an elevation of 30 feet?

Concept Used:

This is a geometric series: $a_1=30;r=95\%=0.95$

The total vertical distances traveled by the ball are the sum of the series.

Because $\left|r\right|=0.95<1$ we use the formula: $\text{S}=\frac{a_1}{1-r}$

Calculation:

This is a geometric series: $a_1=30;r=95\%=0.95$

The total vertical distances traveled by the ball are the sum of the series.

Because $\left|r\right|=0.95<1$ we use the formula: $\text{S}=\frac{a_1}{1-r}$

  $a_1=30;r=0.95;\text{find}\text{S}$

  $\text{S}=\frac{a_1}{1-r}=\frac{30}{1-0.95}=\frac{30}{0.05}=600$

The total vertical distance is 600 feet.

Thus, the total vertical distance is 600 feet.