Shirley is on a Ferris wheel which spins at the rate of 3.6 revolutions per minute. The wheel has a radius of 35 feet, and the center of the wheel is 51 feet above the ground. After the wheel starts moving, Shirley takes 12 seconds to reach the top of the wheel.

Question

How high above the ground is she when the wheel has been moving for 8 minutes?

I know the formula is y(t)=rsin(wt+theta0)+ y0
I got the formula y(t) = 35sin(3.6pi/30 * t + (pi/2 - 3.6pi/30 * 12)) + 51 but when i plugged in 8 I got 53.19766818 but that's not right.. Is my formula off?

Answer 1

since the period is 60/3.6 seconds, and reaches a max at t=12 seconds,

y = 35cos(2pi/(60/3.6)(t-12))+51

which agrees with your formula. You have found y at t=8 seconds, not 8 minutes.