As you ride a Ferris wheel, the height that you are above the ground varies periodically. Consider the height of the center of the wheel to be the equilibrium point. Suppose the diameter of a Ferris Wheel is 42 feet and travels at a rate of 3 revolutions per minute. At the highest point, a seat on the Ferris wheel is 46 feet above the ground.
a. What is the lowest height of a seat?
b. What is the equation of the midline?
c. What is the period of the function?
d. Write a sine equation to model the height of a seat that was at the equilibrium point heading upward when the ride began.
e. According to the model, when will the seat reach the highest point for the first time?
f. According to the model, what is the height of the seat after 10 seconds?