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.
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?
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