The figure below shows an aerial view of The Hurl-O-Matic, a carnival ride in which the passengers are seated in a car, attached to the end of an arm which rotates rapidly around a central hub. Suppose that the length of the arm is 64 feet, and that, at full speed, it takes 10 seconds to for the car to complete one revolution. Find the speed of the car.

A. 40 miles per hour

B. 10 miles per hour

C. 27 miles per hour

D. 21 miles per hour

E. 37 miles per hour

SOLUTION

The distance (D) traveled when the car completes one revolution is the same as the circumference of a circle whose radius is 64 feet.

C = (2)(64)(π) = 402.14 feet

It takes 10 seconds for the car to complete one revolution, so the speed of the car is

402.14 feet/10 seconds = 40.2 feet per second

Now, we need to convert this speed to and equivalent speed in miles per hour.

The fact that the car travels 20.1 feet per second means that in one minute (60 seconds), the car travels

(40.2)(60) = 2412 feet

The fact that the car travels 2412 feet in one minute means that in one hour (60 minutes), the car travels

(2412)(60) = 144,720 feet.

We need to know how many miles the car travels in one hour, so we divide by 5280:

144,720/5,280 = 27.4 miles

Since the car travels 27.4 miles in one hour, its speed is 27.4 miles per hour.

The best answer is C.