Q. 92 - Precalculus Enhanced with Graphing Utilities

Question

A pendulum swings through an angle of ${20}^{\circ }$ each second. If the pendulum is $40$ inches long, how far does its tip move each second? Round answers to two decimal places. 

Step-by-Step Solution

Answer

The tip of the pendulum moves $13.96$ inches each second.

Step 1. Given information

Given, a $40$ inches long pendulum swings ${20}^{\circ }$ in each second.

We consider the movement of a pendulum as a circular motion object.

Step 2. Used formulae

We use the formula $S=r\theta$to obtain the arc length of a circle, where $r$ is the radius and $\theta$ is the angle made by the arc.

Step 3. Conversion of Angles

Given angle ${20}^{\circ }$, when converted to radians, it becomes, $\theta =20·\frac{\mathrm{\pi }}{180}=\frac{\mathrm{\pi }}{9}$

Step 4. Calculation

Substituting the values and using the formulae, 

$s=40·\frac{\mathrm{\pi }}{9}\approx 13.96$ inches.