Ferris wheel, come up with an equation asap please

Question

A Ferris wheel has a radius of 12 meters and takes 16 seconds to complete one full revolution. The seat you are riding in, takes 4 seconds to reach the top which is 28 meters above the ground. Write a sine or cosine equation for the height of your seat above the ground as a function of time

Answer 1

Hannah,

 

Let t be the time in seconds. Since the wheel has a radius of 4 meters and the top of the wheel is 28 meters above the ground, the bottom of the wheel is 4 meters above the ground.

 

The height of the rider on the wheel is given by the function

 

h = 16 − 12 cos θ,

 

where θ is the angle between the radius from the center of the wheel to its bottom and the radius from the center of the wheel to the rider's position. (You can check this by plugging in θ = 0°, 90°, 180°, etc.)

 

The next step is to write the angle in terms of time. You were given the time for the wheel to rotate around once, 16 seconds.  This means that it rotates one revolution every 16 seconds. If you want the formula in terms of degrees, you would use the angular velocity ω = 360°/16 s = 22.5°/s. It is easier to do this in radians, however, where one rotation equals 2π radians. In this case, the angular velocity is ω = 2π/16 = π/8 rad/s.

 

Once you know ω, you can find θ using the formula ω = θ/t. So ... θ = ωt = (π/8)t = πt/8. Once you plug this into the formula above, you will get

 

h = 16 - 12 cos (πt/8).

 

This formula will give the height in meters using time in seconds.

 

The fact that the wheel takes 4 seconds to get the rider to the top really does not make any sense, assuming the wheel rotates at a uniform rate of motion. To get to the top from the bottom, it would take 8 seconds, not 4 seconds.

 

This added bit of information is really irrelevant to the solution and is probably the source of (at least some) of your question.

 

I am sorry for the confusion, but I did not author this question. If you have any questions about my explanation, please feel free to send a reply at your convenience.

Answer 2

f(t) = A sin(Bt - C) + D

f(t) = 12sin((∏/8)t) + 16