Modeling the Motion on Cosmo Clock 21

 

This is Cosmo Clock 21, the giant Ferris wheel located in Minato Mirai. Its height from the

ground is 112.5 meters and it has a rotating diameter of 100 meters. It finishes one rotation

in about 15 minutes.(Source)

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A student rides on Cosmo Clock 21 for two rounds. 

1.Graph this two round-ride modeling the relationship between the student’s height from

the ground with respect to time. 

2. Find a cosine function that is modeling your graph in the form of y=acos(b(x-c))+d.

Show every step explaining how you find a, b, c and d. Explain each variable, including

y and x, how you find them and their meaning in the context of this problem. 

3. At what times will the student be at 100 meter altitude from the ground? Explain.

4.Write a short reflection explaining the degree of your accuracy.

Justify the possible elements or factors making your model and your answer to question

3 inaccurate.

Full solution steps

Some student answers:

y = 50cos((2π / 15) (t - 15/2 )) + 62.5 {0 <= t <= 30 }

y=-50cos(2pi/15)t+62.5 {0<=t<=30}

 Or y=50cos(2pi/15)(t-7.5)+62.5 {0<=t<=30}