Chapter 11, Problem 24PT

To determine

Find the total distance traveled when the pendulum comes to a rest.

Answer to Problem 24PT

Total distance traveled when the pendulum comes to rest is 66.67 inches.

Explanation of Solution

Given:

Laurie swings a pendulum. The distance traveled per swing decreases by 15% with each swing. If the pendulum initially traveled 10 inches, find the total distance traveled when the pendulum comes to a rest.

Concept Used:

This is a Geometric Sequence: $a_1=10;r=1-15\%-1-0.15=0.85$

Calculation:

This is a Geometric Sequence: $a_1=10;r=1-15\%-1-0.15=0.85$

As $\left|r\right|=\left|0.85\right|;0.85<1$ , we can find the sum of the sequence by using this formula $\text{S}=\frac{a_1}{1-r}$

  $\begin{array}{l}{a}_1=10;r=0.85\\ \text{S}=\frac{a_1}{1-r}=\frac{10}{1-0.85}=\frac{10}{0.15}\approx 66.67\end{array}$

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