Question 1173712: A ferris wheel is 35 meters in diameter and boarded from a platform that is 2 meters 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 6 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn.
What is the Amplitude? ? meters
What is the Midline? y = ? meters
What is the Period? ? minutes
How High are you off of the ground after 3 minutes? ? meters
Found 2 solutions by htmentor, ikleyn:
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The general form for the height of the Ferris wheel as a function of time is:
h(t) = Acos(wt) + h0, where h0 is the midline, A is the amplitude, and w = the angular speed in radians per minute.
h(t) oscillates about the midline with an amplitude equal to the radius of the wheel.
The midline, i.e. halfway up, is given by the radius plus h0 = 19.5 m
Thus the amplitude is equal to 17.5 m. Since the initial height must be 2 m,
we have A = -17.5. The angular speed is 2*pi radians per 6 min = pi/3 rad/min.
Thus the equation describing the height is h(t) = -17.5*cos((pi/3)*t) + 19.5
The period, T is given by 2pi/w = 2pi/(pi/3) = 6 min.
h(3) = -17.5*cos(pi) + 19.5 = 17.5 + 19.5 = 37 m (maximum height)
A graph of the function is attached.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
It seems to me, that this problem is for 7year - 8years child, who is not familiar with trigonometry functions.
In any case, they want to get the answers, but do not ask to write the functions.
Actually, this problem has two purposes:
- to check if the reader can read and understand simple geometric facts;
- to combine his (or her) minimal knowledge to get the correct answers.
Following to this style, I'd answer these questions as follows:
- The amplitude is the same as the radius of the wheel.
- The midline is at the height of the axis, i,e 2 + 35/2 = 2 + 17.5 = 19.5 meters.
- The period is given: it is the time of one full rotation/revolution, i.e. 6 minutes.
- The height of a passenger over the ground in three minutes is 2 + 35 = 37 meters.
Solved.
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