The Colossus Ferris wheel debuted at the 1984 New Orleans World’s Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min ride.

Sine function model: where h is the height of the passenger above the ground measured in feet and t is the time of operation of the ride in minutes.

1. What is the period of the sine function model? Interpret the period you found in the context of the operation of the Ferris wheel.

2. The duration of the ride is 15 min.
a. How many times does the last passenger who boarded the ride make a complete loop on the Ferris wheel?
b. What is the position of that passenger when the ride ends?

3. A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes.

a. What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model.
b. Will the last passenger to board the ride need to wait in order to exit the ride? Explain.