Question

Can someone help me with this problem.

-A Ferris wheel has a radius of 37.8 feet. The bottom of the Ferris wheel sits 0.7 feet above the ground. You board the Ferris wheel at the 6 o'clock position and rotate counter-clockwise.

A)Define a function, f that gives your height above the ground (in feet) in terms of the angle of rotation (measured in radians) you have swept out from the 6 o'clock position, a.


B)Define a function, g, that gives your height above the ground (in feet) in terms of the number of feet you have rotated counter-clockwise from the 6 o'clock position, s.

Answer 1

<u>A Ferris wheel has a radius of 37.8 feet.</u>
so, the amplitude is 37.8, and you can start with

f(t) = 37.8 sin(kt)

<u>The bottom of the Ferris wheel sits 0.7 feet above the ground.</u>
So, the axle is 37.8+0.7 = 38.5 feet off the ground:

f(t) = 38.5+37.8 sin(kt)

<u>You board the Ferris wheel at the 6 o'clock position </u>, so instead of being at the axle at t=0, you are at the minimum. That means you need

f(t) = 38.5 - 37.8 cos(kt)

<u>f that gives your height above the ground in terms of the angle of rotation you have swept out from the 6 o'clock position,</u>
Ok. I was thinking f was a function of time. Instead, we need

f(θ) = 38.5 - 37.8 cos(θ)

(B): for g(s), you just need to recall that arc length s=rθ

Answer 2

For the first one, it should be f(a)=37.8(1-cos(a))+.7. My dearest apologies because I do not know why. I just used context from the previous questions. I hope that helps..!

Answer 3

36.2