Question

a ferris wheel with a 40-ft diameter rotates once every 30 seconds. the bottom of the wheel is located 1.5 feet above the ground. you get on at the very bottom of the ferris wheel at time t = 0 and then the ferris wheel begins to turn counter-clockwise. for the problems below, assume the wheel makes 2 full rotations.

a. at what times are you at the top of the ferris wheel? what is the height at the top of the ferris wheel?

b. at what times are you at the bottom of the ferris wheel? what is the height at the bottom of the ferris wheel?

c. at what times are you in the exact middle of the ferris wheel? what is the height of the exact middle of the ferris wheel?

d. write a cosine function to model your height above the ground over time, t.

Answer 1

a. 15, 45, 75, and 105 Seconds.
The elapsed time between each of the 4 numbers is 30 seconds which is
the time for one rev. 15s = 1/2 rev.
h = 1.5 + 40 = 41.5 Ft. above gnd.

b. 30, 60, 90, and 120 Seconds.
h = 1.5Ft. above gnd.

c. (3/4)rev * 30s/rev = 22.5 s.
22.5, 52.5, 82.5, and 112.5 Seconds.
h = 1.5 + 0.5*40 = 21.5 Ft.

Answer 2

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