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# Periodicity

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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: h = -82.5 cos 3π(t) + 97.5 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) 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 it's a lot but I haven't been able to find help anywhere else and I actually need to understand how to solve this, please show all work please!)

Apr 24, 2021

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As follows:

Apr 24, 2021
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Thank you so much, I really appreciate it :)

Corduroy  Apr 24, 2021
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May I ask 1 question? 'm sorry I just don't completely understand~! I get that you divided 15(2/3) but does this mean that the last person who boarded the Ferris wheel completed 22 loops or...?

And for 2b, how does 15/T = 22.5 prove that the passenger is halfway through the rotation?

Thank you :)

Corduroy  Apr 24, 2021
edited by Corduroy  Apr 24, 2021
edited by Corduroy  Apr 24, 2021
edited by Corduroy  Apr 24, 2021
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The question 2a asks how many complete loops were made.  This has to be a whole number.  So, if 15/T is not a whole number (which it isn't) we need to take the nearest whole number less than this.  That is what the floor function does.

For 2b, we see that 15/T is 22.5, which means the passenger does 22 complete loops, plus half of a loop.  Since the passenger starts at the bottom, 22 complete loops will leave him/her at the bottom, and another half loop will take them to the top.

Alan  Apr 24, 2021
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I understand now, thank you!

Corduroy  Apr 24, 2021