Problem:
Riders on a Ferris wheel travel in a circle in a vertical plane. A particular wheel has radius feet and revolves at the constant rate of one revolution per minute. How many seconds does it take a rider to travel from the bottom of the wheel to a point vertical feet above the bottom?
Answer Choices:
A.
B.
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E.
Solution:
In the figure, the center of the wheel is at , and the rider travels from to . Since and , the point is the midpoint of . In the right , we have half of the length of the hypotenuse , so . Since the wheel turns through an angle of in seconds, the time required to turn through an angle of is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions