Question

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Answer 1

Answer:

  h = f(t) = -15cos((π/5)t) +20

Step-by-step explanation:

If you like, you can make a little table of positions:

  (t, h) = (0, 5), (5, 35)

Since the wheel is at an extreme position at t=0, a cosine function is an appropriate model:

  h = Acos(kt) +C

The amplitude A of the function is half the difference between the t=0 value and the t=5 value:

  A = (1/2)(5 -35) = -15

The midline value C is the average of the maximum and minimum:

  C = (1/2)(5 + 35) = 20

The factor k satisfies the relation ...

  k = 2π/period = 2π/10 = π/5

So, the function can be written as ...

  h = f(t) = -15cos((π/5)t) +20