A Ferris wheel is 27meters 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 16minutes. 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 44 minutes?