precalculus homework help

Question

A Ferris wheel is 40 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. How many minutes of the ride are spent higher than 43 meters above the ground?

= mins

detailed help please

Answer 1

First, the radius r=20.

Since the wheel is 4 meters above the ground, the ride only need to be at least 43-4-20=19 meters higher than the center of the wheel to satisfy the requirement.

Let A be the top point of the wheel, O be the center of the wheel, and B be a point on the wheel which is 19 meters above the center O. Let t be the time the ride spent higher than 43 meters above the ground. Then,

cos(∠AOB)=19/20.

t/4=2 × ∠AOB/2π.

t=4 × ∠AOB/π

=4 × arccos(19/20)/π

=0.4 min