Answer: H = 30ft*cos(2*pi*t/48s + pi) + 38ft.
Step-by-step explanation:
We can use a trigonometric function to model this, let's use:
H = A*cos(w*t) +
where A is a constant, w is the frequency, t is time, and h is of the wheel, this is half the diameter plus the distance above the ground:
30ft + 8ft = 38ft.
A is equal to the radius of the wheel, or half the diameter, A = 60ft/2 = 30ft.
we know that the period is 48 seconds, this means that:
cos(w*0) = cos(w*48s) = 1
then w*48s = 2*pi
w = 2*pi/48s
so now function is:
H = 30ft*cos(2*pi*t/48s) + 38ft.
But we also know that, at t= 0, you must be at the bottom of the wheel, so we must ad a phase of pi to the cosine function
H = 30ft*cos(2*pi*t/48s + pi) + 38ft.
So now when t = 0, we have:
H(0) = 30ft*cos(0 + pi) + 38ft. = 8ft.