A Ferris wheel has a radius of 11 meters and the bottom of the Ferris wheel is 1

Question

A Ferris wheel has a radius of 11 meters and the bottom of the Ferris wheel is 1 meters above the ground. Elliot boards the Ferris wheel at the 3 o'clock position. The Ferris wheel rotates at a constant speed of s radians per second.

a. Write a formula that gives the angle measure, a, (in radians) swept out from the 3 o'clock position in terms of the number of seconds elapsed, t, since Elliot boarded the Ferris wheel.

b. Write a formula that gives the period, p (in seconds) in terms of the speed of the Ferris Wheel, s (in radians per second).

c. Write a formula that gives Elliot's height above the ground, h, (in meters), in terms of the number of seconds elapsed, t, since Elliot boarded the Ferris wheel.

Explanation / Answer

a) constant speed of s radians per second

angle measure , a = s*t (radians)

b) Period = time for one revolution p = 2pi/s

c) h(t) = 12 -11sin(st)

at st=0; h(0) = 12 --->3 'o clock position

at st = 90 deg ; h(t) = 12 -11 = 1mt

at st = 180 deg ; h(t) = 12 -0 = 12 mt

at st= 270 deg h(t) = 12+11 = 23 mt

So, h(t) =  12 -11sin(st)

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