How many minutes of the ride are spent higher than 27 meters above the ground?

Question

A Ferris wheel is 35 meters in diameter and boarded from a platform that is 2 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 6 minutes.

Answer 1

Start with a diagram.

We're going to need to find an angle so we can find which part of the arc of the circle is above this height.

Radius = 35/2 = 17.5

Height from center = 27 - 2 - 17.5 = 7.5, which will be the adjacent side of our angle θ.

θ = cos^-1 (7.5/17.5) = 64.6°

2θ = 129.2° (for the right and left of center portions)

Now we find the fraction of the 6 minute rotation proportional to the angle.

6 minutes * 129.2/360 = 2.15 minutes or 2:09.