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A Ferris wheel is 21 meters in diameter and completes 1 full revolution in 12 minutes.

A round Ferris wheel

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).

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 45 minutes?

Sagot :

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