A Ferris wheel is 25 meters in diameter and boarded from a p

A Ferris wheel is 25 meters in diameter and boarded from a platform that is 5 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 2 minutes. How many minutes of the ride are spent higher than 26 meters above the ground

Solution

Since the bottom of the wheel is 5m above ground, a rider is higher than 26 m above ground when the rider is higher than 21 m above the bottom of the wheel.

21 m above the bottom of the wheel is
21 - (25/2) = 21 - 12.5 = 8.5m above the horizontal line passing through the center of the wheel.
Thus, the tangent of the central angle of the wheel at which one passes 26m above ground is
8.5/12.5 = 0.68
and arctan0.68 = 34.2 degrees.

The portion of a circle of the wheel above that height is therefore
(180 - 2 * 34.2)° = 111.6°,
which is
111.6°/360° = 0.31 of a circle,
and will occupy about 0.62 minutes of a 2-minute revolution.