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Question

A Ferris wheel is 21 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 12 minutes. The function h(t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn.

a. Find the amplitude, midline, and period of h(t).

b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t=0. Find a formula for the height function h(t).

c. If the Ferris wheel continues to turn, how high off the ground is a person after 33 minutes?

Answer 1

desmos.com/calculator/rlolri5hu9

Use the moving point on the graph of h(x) to see the ferris wheel car go through its revolutions.

Answer 2

ferris wheel is 21 meters in diameter, it's platform is 1 meter above the ground

the wheel completes 1 full revolution every 12 minutes.

h(t) gives a person's height at time t where t is measured in minutes and h in meters

at t=0, h= 1

general formula is h(t) = Asin(Bt+C) + D where A = Amplitude= (1/2)(max+min) = 5.25, D = midline= A +1 = 6.25, C= phase shift=-pi/2, 2pi/B=period=12 minutes, B= 2pi/12=pi/6=frequency

h(t) = 5.25sin[(2pi/12)(t)-pi/2] + 6.25

= 5.25sin(pi/6 - pi/2) +6.26

in 33 minutes the person is h(33) = 5.25sin([pi/6)(33) -pi/2] + 6.25 meters high

= 5.25sin(11pi/2 -pi/2) +6.25 = 5.25sin5pi + 6.25 = 5.25sinpi+6.25 = 0+6.25 = 6.25 meters high

You could have described the height in terms of cosines instead of sines, but the phase shift would be different

this problem should have been listed under "trigonometry" Then you might have received more answers

when B=1, the period = 2pi

when B=2 the period = pi

let p=the period, B = 2pi/p = 2pi/12= pi/6= frequency