Answer to Question #122060 in Trigonometry for melanie zhou

Question

Given the information below determine an equation for the sinusoidal function.

Time for 1
Rotation (in s): 100
Lowest Point
of the Bucket
(in m): 1.6m
Diameter of
Ferris Wheel
(in m):42 m
Number of
Buckets: 16

Answer 1

Determine a sinusoidal equation for the height of the bottom of the bucket above the ground $H(t)$. The amplitude will be equal to the radius of the Ferris wheel:

$$R=A.$$

The time required for one rotation is the period. The period allows us to find the angular frequency:

$$\omega=2\pi f=\frac{2\pi}{T}=\frac{\pi}{50}.$$

The function is

$$H(t)=h_0+A\text{ sin}(\omega t),\\ H(t)=R+A\text{ sin}\bigg(\frac{2\pi}{T} t\bigg),\\\space\\ H(t)=21\bigg[1+\text{ sin}\bigg(\frac{\pi}{50} t\bigg)\bigg]\text{ m}.$$

As we see in the image, the lowest point of the bucket does not matter because the height of the bottom of the buckets also makes circles (grey) with radius equal to the radius of the Ferris wheel: