Question

A Ferris wheel has a radius of 35m and starts at 2m above the ground. It rotates once
every 53 second. a) determine the cosine equation of the graph, if the rider gets on at
the lowest point. b) what is the height of the rider at 81 seconds?

Answer 1

Let t be time in seconds and y(t) the height in meters. The center height is 2 + 35 = 37 m, amplitude 35, period 53 s, and the rider is at the minimum when t = 0. A convenient cosine model is

y(t) = 37 − 35 cos(2πt/53).

At t = 81 s,
y(81) = 37 − 35 cos(162π/53) ≈ 71.45 m (rounded).