A chair on the wheel is undergoing circular motion with a radius of 10 meters (d/2) and a period of 5 minutes. The y position based solely on a circle that is centered at 0 is
y(t) = rsin(2πt/T-π/2) (The - pi/2 adjusts for starting time at the bottom rather than at the 0 angle which corresponds to the level of the x axis)
This Ferris wheel is centered 12 meters above the ground. So the equation becomes
Y(t) = 12 + 10sin(2πt/5-π/2) with t in minutes (t = 0, Y=2 and t=T/2, Y=22)
You could also use Y(t) = 12 -10cos(2πt/5)
Now you want to solve for t so that Y(t) ≥ 14 m
Rearranging to solve for t
t = (5/(2π))(sin-1((Y-12)/10)+π/2) = 1.410 min for Y=14
You know that the sin function will be higher than 14 until the maximum sin value at t = 2.5 min
The time above 14 should be 2(2.5-t(Y=14)) min
Hopefully, I got it all right. Please review it. Take care.
