Question

Could you please look at this question?

Answer 1

Answer:

  a. see attached

  b. H(t) = 12 -10cos(πt/10)

  c. H(16) ≈ 8.91 m

Step-by-step explanation:

a.

The cosine function has its extreme (positive) value when its argument is 0, so we like to use that function for circular motion problems that have an extreme value at t=0. The midline of the function needs to be adjusted upward from 0 to a value that is 2 m more than the 10 m radius. The amplitude of the function will be the 10 m radius. The period of the function is 20 seconds, so the cosine function will be scaled so that one full period is completed at t=20. That is, the argument of the cosine will be 2π(t/20) = πt/10.

The function describing the height will be ...

  H(t) = 12 -10cos(πt/10)

The graph of it is attached.

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b.

See part a.

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c.

The wheel will reach the top of its travel after 1/2 of its period, or t=10. Then 6 seconds later is t=16.

  H(16) = 12 -10cos(π(16/10) = 12 -10cos(1.6π) ≈ 12 -10(0.309017) ≈ 8.90983

The height of the rider 6 seconds after passing the top will be about 8.91 m.