Chapter 13.1, Problem 6MRE

To determine

To find: The speed of a seat on the rim.

Answer to Problem 6MRE

The speed of a seat on the rim is $160\pi$ ft/min.

Explanation of Solution

Given information:

The given merry-go-round $40$ ft in diameter makes four revolution every minute.

Calculation:

Calculate the speed.

The seat on the rim of the merry-go-round covers its perimeter $\left(2\pi r\right)$ in $1$ revolution.

That it is covers $40\pi$ in $1$ revolution.

This indicates that it must cover $160\pi$ in four revolutions.

Thus,

  $\begin{array}{l}v=\frac{s}{t}\\ v=\frac{160\pi }{1}\\ v=160\pi \text{ ft}/\min \end{array}$

Therefore, the speed of a seat on the rim is $160\pi$ ft/min.