Q. 50 - Precalculus Enhanced with Graphing Utilities

Question

The minute hand of a clock is $8$ inches long. How far does the tip of the minute hand move in $30$ minutes? How far does it move in $20$ minutes?

Step-by-Step Solution

Answer

The distance travelled is $25.13in,16.76in$

Step 1: Given information

Given minute hand is eight inches long

Step 2: Use the formula for arc length and calculate the value

Calculate the value, we get

$$\begin{gathered} s=r\theta \\ s=8in·\pi \\ s=25.13\mathrm{in} \end{gathered}$$

Then,

$$\begin{gathered} s=r\theta \\ s=\sin ·\frac{2\pi }{3} \\ s=16.76\mathrm{in} \end{gathered}$$