Chapter 11.3, Problem 61PPS

To determine

Find the total distance traveled by the pendulum after the 30^th swing.

Answer to Problem 61PPS

About 471 cm

Explanation of Solution

Given:

The first swing of a pendulum travels 30 centometers. If each subsequent seing travels 95% as fas as the previous swing, find the total distance traveled by the pendilum after the 30^th swing.

Concept Used:

Given: $a_1=30\text{cm};r=95\%,n=30$

Calculation:

Given: $a_1=30\text{cm};r=95\%,n=30$

Now find the sum:

  $\begin{array}{l}{a}_1=30\text{cm};r=95\%=0.95,n=30;\text{find}{\text{S}}_{\text{n}}\\ {\text{S}}_{\text{n}}=\frac{a_1(1-r^n)}{1-r}\\ {\text{S}}_{\text{n}}=\frac{30(1-{0.95}^{30})}{1-0.95}\approx 471\end{array}$

Thus, the distance travelled is about 471 cm.