Chapter 12.5, Problem 9P

To determine

Find the angle through which the pendulum swing.

Answer to Problem 9P

  $23.4°$

Explanation of Solution

Given:

A pendulum in a grandfather clock is 160 cm long.The horizontal distance between the farthest points in a completer swing is 65 cm.

Formula Used:

  $\sin \theta =\frac{\text{length of opposite side to }\theta }{\text{length of }hypotenuse}$

Calculation:

Represent the given situation

  

We need to find x .

Use the sin formula :

  $\begin{array}{l}\sin \frac{x}{2}=\frac{\text{length of opposite side to }\frac{x}{2}}{\text{length of }hypotenuse}\\ \Rightarrow \sin \frac{x}{2}=\frac{\raisebox{1ex}{$65$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{160}\\ \Rightarrow \frac{x}{2}={\sin }^{-1}(0.2031)\mathrm{...............}[\text{take inverse of sin each side]}\\ \Rightarrow \frac{x}{2}=11.72°\\ \Rightarrow x=23.4°\end{array}$

So, the angle through which the pendulum swing is $23.4°$ .