A Ferris wheel is 24 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 8 minutes. The function h(t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn.
A Ferris wheel is 24 meters in diameter and completes 1 full revolution in 8 minutes.
A Ferris wheel is 24 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 8 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).
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 time t=0. Find a formula for the height function h(t).
Hints:
- What is the value of h(0)?
- Is this the maximum value of h(t), the minimum value of h(t), or a value between the two?
- The function sin(t) has a value between its maximum and minimum at t=0 , so can h(t) be a straight sine function?
- The function cos(t) has its maximum at t=0, so can h(t) be a straight cosine function?
c. If the Ferris wheel continues to turn, how high off the ground is a person after 20 minutes?
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