A Ferris wheel is 2929meters in diameter and boarded from a platform that is 11 meter above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 11 full revolution in 1212minutes. The function h(t)ht gives a person's height in meters above the ground tt minutes after the wheel begins to turn.

a. Find the amplitude, midline, and period ofh(t)ht.

Enter the exact answers.

Amplitude:A=A= meters

Midline:h=h= meters

Period:P=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=0t=0.Find a formula for the height function h(t)ht.

Hints:

• What is the value ofh(0)h0?
• Is this the maximum value ofh(t)ht, the minimum value ofh(t)ht, or a value between the two?
• The functionsin(t)sinthas a value between its maximum and minimum at t=0t=0, so canh(t)htbe a straight sine function?
• The functioncos(t)costhasits maximum at t=0t=0, so canh(t)htbe a straight cosine function?

c. If the Ferris wheel continues to turn, how high off the ground is a person after 3939 minutes?