Ferris wheel problem

Question

A Ferris wheel has a radius of 33.6 feet. The bottom of the Ferris wheel sits 0.6 feet above the ground. You board the Ferris wheel at the 6 o'clock position and rotate counter-clockwise.

1: Write a function, that determines your height above the ground (in feet) in terms of the number of feet you have traveled since you started rotating

Answer 1

Let

r = 33.6 ft be the radius of the Ferris wheel,

h = 0.6 ft be the height of the bottom of the wheel,

s be some distance you travelled measured along the circle of the wheel,

y(s) be your height above ground after traveling distance s.

After traveling distance s, the spoke connecting your cabin to the center forms an angle

s/r with the vertical.

Therefore you are distance rcos(s/r) below the horizontal.

Therefore you are distance r - rcos(s/r) from the bottom of the wheel.

Therefore your distance from the ground is

y(s) = h + r(1 - cos(s/r))