Question
A Ferris wheel is 30meters in diameter and boarded from a platform that is 1 meter above the ground. The six o'clock position on the
A Ferris wheel is 30meters 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 12minutes. 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 ofh(t).
Enter the exact answers.
Amplitude:A= ......... meters
Midline:h=........ meters
Period:P=......... minutes
b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at timet=0.Find a formula for the height function h(t).
Hints:
- What is the value ofh(0)?
- Is this the maximum value ofh(t), the minimum value ofh(t), or a value between the two?
- The functionsin(t)has a value between its maximum and minimum at t=0, so canh(t)be a straight sine function?
- The functioncos(t)hasits maximum at t=0, so canh(t)be a straight cosine function?
c. If the Ferris wheel continues to turn, how high off the ground is a person after 45 minutes?
please provide with explanation
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