Trig Ferris Wheel Problem

Question

Part 1

The Ferris Wheel has a diameter of 30 meters, the center is 19 meters off the ground and it makes 2 revolutions per min.

Draw this Ferris Wheel, labeling the radius, height, and center. Supposing the minimum height of the Ferris Wheel occurs when t=0, write the sinusoidal function for the height as a function of time. Last graph on a coordinate plane, label the key points.

Part 2

Design your own Ferris Wheel, determining diameter, center, and speed. Write the function for the height of the Ferris Wheel as a function of time. Is your Ferris Wheel realistic? Does it travel too fast or too slow?

Answer 1

Since the function starts at the bottom and goes up, it's easily modeled as a negative cosine function so:

y = -Acos(Bt)+C

A is the amplitude (in this case A = 15)

B is what defines the period. Since there are 2 revolutions per minute, each cycle completes in half a minute so the period = 0.5. The value of B is 2π/Period = 2π/0.5 = 4π.

C = the vertical shift, in this case C = 19.

So the function is h(t) = -15cos(4πt) + 19 where t is in minutes and h is in meters

Answer 2