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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?

1. 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 is the height of the last passenger above the ground measured in feet and is the time of operation of the ride in minutes.
• What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model.
• Will the last passenger to board the ride need to wait in order to exit the ride? Explain.

Jul 24, 2021

#1
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There is a good explanation here:

https://web2.0calc.com/questions/periodicity

Jul 24, 2021
#2
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1.

(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  !!!

Jul 24, 2021
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Thanks for the help!

hippobush2  Jul 26, 2021