Sinusoidal Ferris Wheel

Question

The height of the axle is 20 meters tall. The diameter of the wheel is 30 meters wide. The wheel turns clockwise.

a. If a person gets on the wheel at the very bottom of the wheel, how high off the ground will they be?

b. How high off the ground will they be half way up the wheel?

c. How high off the ground will they be at the top of the wheel?

d. How high off the ground will they be half down the wheel?

e. The Ferris wheel takes 6 minutes for a full rotation. Complete the table below. *Note you must convert to seconds. (6 minutes = _______ seconds)

Answer 1

Use this in conjunction with the other tutor's (Terrance S.) answer:

The period is 6 minutes so you could create an equation for the height of a person riding on the Ferris Wheel by using:

h(t) = -15cos[(2π/6)t] + 20

Answer 2

Man I wish I could make a diagram and upload it

Alright Jay check it out:

Remember the diameter is 30m meaning the radius is 15m . . .

The radius is what u want to focus on. but the center of the ferriswheel (which is the axle) is 20 m off the ground.

So to "a" answer a goes like this:

So at the very bottom (where people get on) would have to be 5m off the ground. Bcz it's the height of the center which is 20m - 15m which is the radius.

So the 5m comes from the difference of the height of the center (or axle) which is 20m and the distance of radius which is 15m. 20 - 15 = 5.

The radius is gonna be 15 no matter what position the ferriswheel is in. Keep that in mind. Now you should be able to answer b c d and e.