Question

A ferris wheel is 50 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 4 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? meters

What is the Midline? y = meters

What is the Period? y = minutes

How High are you off of the ground after 2 minutes? meters

Answer 1

This is a case of sinusoidal variation since you are dealing with a linear distance in the vertical as something goes around a circle.

The minimum height is given as 3 meters, and the diameter of the wheel is given as 50 meters. So we know that the maximum height is 53 meters and the middle is 26.5meters, meaning that the height is going to vary by 25meters (half the diameter) above and below 26.5 meters.

The minimum height is at time zero, the maximum height is when the wheel has gone half-way around, which is to say at time 2 minutes, and the minimum height is again reached at 4 minutes.


varies from to and back to as varies from to .

So varies from to and back to as varies from to .

So varies from to and back to as varies from to

Now if we want to measure the period as an amount of time, then we need a factor when multiplied by the period time, , gives so that we can write:

now we have the necessary values to create the function:

The centerline value c = 26.5

The magnitude of the displacement from the centerline: a 25.0

The lead coefficient sign, because the function is at a minimum at time zero,

And the periodicity factor: b= π/2

Putting it all together

h(t) = –25cos(πt/2) + 26.5

The time period is 4

And at time 2 minute

The h(t) = –25cos(π*2/2) + 26.5

h(t) = –25(–1) + 26.5

h(t) = 25 + 26.5

h(t) = 51.5 meters