A ferris wheel is 25 meters in diameter and boarded from a platform that is 1 meters above the ground.

Question

A ferris wheel is 25 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 2 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).

F(t) =

Answer 1

Since the function starts low and goes up to the highest point, it seems like a negative cosine function would be the easiest approach. The generic version of that is y = -Acos[B(x - C)] + D where A is the amplitude, B is 2π/Period, C is the phase shift (aka horizontal shift) and D is the vertical shift.

In this case the amplitude (A) is 12.5 meters (the radius) because from its center the highest point is 12.5 meters up and the lowest point is 12.5 meters down.

In this case, B = 2π/2 because the period is 2 minutes so B = π.

In this case, there is no phase shift so C = 0

In this case, D = 12.5 + 1 since the center of the Ferris wheel is that far off the ground so D = 13.5

That makes the function: h = f(t) = -12.5cos(πt) + 13.5