Solve the problems below.

A Ferris wheel is 25 meters in diameter and completes 1 full revolution in 8 minutes.

A round Ferris wheel

A Ferris wheel is 25 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= Number meters

Midline: h= Number meters

Period: P= Number 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 18 minutes?