Chapter 11.4, Problem 28PPS

To determine

Find the total distance traveled when he comes to rest.

Answer to Problem 28PPS

66.67 inches

Explanation of Solution

Given:

If Kerry foes not push any harder after his initial swing, the distance traveled per swing will decrease by 10% with each swing. If his initial swing traveled 6 feet, find the total distance traveled when he comes to rest.

Concept Used:

The problem based on geometric sequence.

  $a_1=10;r=1-0.15=0.85$

We find the sum of the sequence (we can do this because $\left|r\right|=\left|0.85\right|\Rightarrow 0.85<1),$ using the formula : $S=\frac{a_1}{1-r}$

Calculation:

The problem based on geometric sequence.

  $a_1=10;r=1-0.15=0.85$

We find the sum of the sequence (we can do this because $\left|r\right|=\left|0.85\right|\Rightarrow 0.85<1),$ using the formula : $S=\frac{a_1}{1-r}$

  $S=\frac{a_1}{1-r}=\frac{10}{1-0.85}=\frac{10}{0.15}\approx 66.67$

The total distance traveled when he comes to rest is 66.67 inches.

Thus, the total distance traveled when he comes to rest is 66.67 inches.