Question

9. A Ferris wheel makes 1 revolution per minute. The linear speed of the seats on the rim of the wheel is 2.14 mph. To the nearest foot, find the radius of the Ferris wheel.

Answer 1

Given:

A Ferris wheel makes 1 revolution per minute, n = 1 rpm

so, the angular speed :

$\omega=\frac{2\pi\cdot n}{60}=\frac{2\pi\cdot1}{60}=\frac{\pi}{30}$

The linear speed of the seats on the rim of the wheel is 2.14 mph

so,

$\begin{gathered} v=\omega\cdot r \\ \end{gathered}$

convert from mph to ft/sec

hour = 3600 sec

mile = 5280 ft

so,

$2.14\frac{mile}{hour}=2.14\cdot\frac{5280}{3600}\frac{ft}{\sec}=\frac{1177}{375}\frac{ft}{\sec }$

so,

$\begin{gathered} \frac{1177}{375}=\frac{\pi}{30}\cdot r \\ \\ r=\frac{30\cdot1177}{375\pi}=29.97 \end{gathered}$

So, the answer To the nearest foot is r = 30 ft