A Ferris wheel with a diameter of 57 meters rotates at a rate of 4 minutes per revolution. Riders board the Ferris wheel 5 meters above the ground at the bottom of the wheel. A couple boards the Ferris wheel and the ride starts.

Question

Write a formula for the height of the couple t seconds after the ride begins.

How many seconds after the ride starts will the couple be 40 meters above the ground for the second time?

Answer 1

the people board at the lowest point, so we can start with
y = -Acos(kt)
diameter of 57, so A = 28.5
y = -28.5cos(kt)
Riders board the Ferris wheel 5 meters above the ground at the bottom of the wheel, so
y = 33.5 - 28.5cos(kt)
4 minutes per revolution so the period is 4
cos(kt) has period 2π/k = 4, so k = π/2
y = 33.5 - 28.5 cos(π/2 t)
So now just solve
33.5 - 28.5 cos(π/2 t) = 40
and take the second solution in [0,4]
t = 2.85 min