Ferris Wheel Example (continued)
Here is a drawing of the Ferris wheel:
You can use the general equation y = Asin(kt - c) + h to find the sinusoidal function of this Ferris wheel.
Amplitude, or A, is the radius of the Ferris wheel.
To find k, you can use the fact that the period is equal to 4.5 minutes.
There is no phase shift because at t = 0 the seat is at the midline.
To find h, you need to find the bottom of the Ferris wheel. You know that the total height is 65.5 meters and the diameter is 61.5 meters. To find the bottom portion of the Ferris wheel, you can subtract the diameter of the Ferris wheel from the total height.
65.5 – 61.5 = 4 meters
The value of h at the midline is the amplitude plus the bottom of the Ferris wheel.
30.75 + 4 = 34.75 meters
The final equation is:
