A ferris wheel is 10 meters in diameter and boarded from a platform that is 3 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 8 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).
Question
A ferris wheel is 10 meters in diameter and boarded from a platform that is 3 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 8 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).
Solution
The height of a point on a Ferris wheel as a function of time can be modeled by a sinusoidal function, specifically a cosine function because the height starts at its minimum.
The diameter of the Ferris wheel is 10 meters, so the radius is 5 meters. This is the amplitude of the function.
The Ferris wheel is 3 meters above the ground, which is the vertical shift of the function.
The period of the function is the time it takes for the Ferris wheel to make one full revolution, which is 8 minutes.
The function for the height of a point on the Ferris wheel as a function of time is:
h(t) = 5cos(2πt/8) + 8
This function gives the height in meters of a point on the Ferris wheel t minutes after the wheel begins to turn.
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