Question 1040000: A ferris wheel is 15 meters in diameter and boarded from a platform that is 2 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 6 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
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 2 meters, and the diameter of the wheel is given as 15 meters. So we know that the maximum height is 17 meters and the middle is 9.5 meters, meaning that the height is going to vary by 7.5 meters (half the diameter) above and below 9.5 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 3 minutes, and the minimum height is again reached at 6 minutes.
Now we can create a picture of the function:
.jpg) .
) varies from  to  and back to as  varies from  to  .
So ) varies from  to  and back to as varies from to .
So \ +\ c) 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:
\ =\ -a\cos\left(bt\right)\ +\ c)
The last thing we need is a value for :
So now we have the necessary values to create the function:
The centerline value: 
The magnitude of the displacement from the centerline: 
The lead coefficient sign,  because the function is at a minimum at time zero,
And the periodicity factor: 
Putting it all together
\ =\ -7.5\cos\left(\frac{\pi}{3}t\right)\ +\ 9.5)
John
My calculator said it, I believe it, that settles it
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