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 20 vertical feet above the bottom?
In one minutes, the wheel has spun once, so it has traveled \(40pi\) feet.
So we have: 60 sec. = 40 pi feet, so ? sec. = 20 feet.
So ? = 60/2pi = 30/pi sec.
30/3pi is about 9.55. So to the nearest integer, the answer is 10.
If we imagine a circle with an equation of x^2 + y^2 = 20^2
The coordinates at the bottom of the wheel = (0, -20)
When the wheel is 20 vertical feet from the bottom (assuming a counter-clockwise rotation) it is at (20, 0)
This position represents a 1/4 turn of the wheel ......so....it must take the wheel (1/4) (60) =15 seconds to reach this point