Precalculus Question:

Question

A ferris wheel is 15 meters in diameter and boarded from a platform that is 2 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 10 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

Thinking about this, at time t = 0 we will get on and be at the lowest point on the travel. This is best modeled by a negative cosine function, which starts on the y-axis at -1 and goes up to +1 and then back down to -1 (the lowest point).

So our basic function would be h(t) = -Acos[B(t - C)] + D

where A is the amplitude, B is 2π/period, C is the phase shift, and D is the vertical shift.

In this case the amplitude (A) is the radius because the height goes up and down by that much. Since the diameter is 15, the radius is 7.5 so A = 7.5

To calculate B, we need the period, We are told that one revolution is 10 minutes so the period is 10 meaning B = 2π/10 = π/5

In this case, since the smallest height is at t = 0, there is no phase shift so C = 0

The vertical shift is how far the mid-line shifts up. In this case, it shifts up by 2 meters to the platform then 7.5 meters to to the middle of the Ferris wheel. So D = 9.5

Putting this together: h(t) = -7.5cos[(π/5)t] + 9.5