Chapter 13.4, Problem 59STP

To determine

To find: The total distance that the pendulum swings before it stops.

Answer to Problem 59STP

The total distance travelled by the pendulum is $96cm$ .

Explanation of Solution

Given information:

Pendulum swings $24$ centimeters to the other side, then $18$ centimeters back and $13.5$ centimeters and so on.

Pendulum swings $24$ centimeters to the other side, then $18$ centimeters back and $13.5$ centimeters and so on.

This represents the below series

  $24,18,13.5,\mathrm{....}$

This is a Geometric series.

Sum of infinite terms of Geometric series $S=\frac{a}{1-r}$

From above series

We can say that

  $a=24$

Common ratio $=r=\frac{18}{24}=\frac{13.5}{18}=0.75$

On substituting values

We get

  $\begin{array}{l}S=\frac{a}{1-r}\\ \Rightarrow S=\frac{24}{1-0.75}\\ \Rightarrow S=\frac{24}{0.25}\\ \Rightarrow S=96\end{array}$

Therefore,

The total distance travelled by the pendulum is $96cm$ .