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. 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?
I know its long but I dont know how to solve it please help me!
There is a good explanation here:
(a) The ride completes a loop every 40 sec and 3 complete loops in two minutes
So...... 15 mintues = 900 sec
So the number of complete loops in this time frame = floor [ 900/40] = 22 complete loops
(b) When the ride ends we look at the position at 15 min.....note that the height at this point = 180 ft
At 6 min after the ride started note that the height of the last passenger to board = 15 ft
6min = 360 sec
This makes sense.....he'she will have completed = floor [ 360 / 40 ] = 9 complete loops at this point
He/she will exit at its lowest point at the 6 minute mark....so.....no waiting !!!