Question

Riders on a Ferris wheel travel in a circle in a vertical plane. A particular wheel has radius $20$ 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 $10$ vertical feet above the bottom?

$5$

$6$

$7.5$

$10$

$15$

Solution:

Put the center $O$ at height $20.$ The bottom $A$ is at height $0,$ and the rider reaches height $10,$ which is $10$ feet below the center.

The horizontal from the center down to the rider's level forms a right triangle where the vertical leg is $10$ and the hypotenuse (the radius) is $20.$ That leg is half the hypotenuse, so the radius to the rider makes $60^\circ$ with the downward vertical.

The wheel turns $360^\circ$ in $60$ seconds, so turning $60^\circ$ takes $\dfrac{60}{360}\cdot 60 = 10$ seconds.

Thus, the correct answer is D.

2002 AMC 10B Problem 24

Solution:

Problem 24 in Other Years