I need these pls

Question

A Ferris wheel has a diameter of 60ft. When you start at the top of the Ferris wheel, you are 62 ft from the ground. The Ferris wheel completes one rotation in 2 minutes.

1)create a function the represents your height from the ground as a function of time.

2)If the Ferris wheel stops after 8.5 minutes, how high from the ground would you be? Use the function from above and show the work.

3)The Ferris wheel starts again from the position in the last question, resetting time to=0. Create a graph that represents you height relative to the ground as a function of time, show a graph.

4)create a new function of the height from the ground as a function of time for the situation in the last question.

Answer 1

1) Assuming you start at the top, then we would use a cosine function (it start at 1 and goes down then back up just like this Ferris wheel).

The generic format for a cosine function is:

h(t) = Acos(B(t - C)) + D

where:

A is the amplitude (distance from the neutral point, in this case the center of the Ferris wheel) to the max or min. So in this case A = 30

B is the number that is used to calculate the period (time for a complete cycle. B = 2π/Period so in this case B = 2π/2 or B = π

C = the phase shift or time shifted from the normal cosine function. In this case that is zero because we are starting at the top at time t = 0 and that's what cosine does.

and D is the vertical shift, in this case D = 32 feet (distance from the ground to the middle.

That makes the function:

h(t) = 30cos(πt) + 32 where t is in minutes and h is in feet

2) h(8.5) = 30cos(π•8.5) + 32 = 30•0 + 32 = 32 feet (right in the middle)

For 3), since the graph strats in the middle, let's switch to a sine function since sine starts at 0 then goes up and down and back to zero, just like this case.

So, the same generic equation applies, just switch to sine:

h(t) = 30sin(πt) + 32.

The graph would look like this: