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At the state fair, the giant Ferris wheel takes 48 seconds to make one full rotation. The Ferris wheel has a diameter of 60 ft. and the bottom of the wheel is 8 ft. above the ground. If you are the last person on the Ferris wheel and you board at the bottom, which equation below models your height above the ground as a function of time?

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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.

[tex]\rm H = 30cos \frac{2 \pi t}{48} + 38 \ ft.[/tex] is the obtained equation below model your height above the ground as a function of time.

What is the equation?

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Given data;

A is a constant,

ω is the frequency

t is the passage of time

h is the wheel's height,

d is the diameter

h = d/2

The equation for the SHM is found as;

y = Acosωt

For the given condition the equation is written as;

H = Acosωt

The distance above the ground;

30ft + 8ft = 38ft.

⇒cos(ωt)

⇒cos(w × 48) = 1

⇒ω×48s = 2π

⇒w = 2π/48s

The obtained function is;

[tex]\rm H = 30cos \frac{2 \pi t}{48} + 38 \ ft.[/tex]

We must add a phase of π to the cosine function since we also know that at time t=0, you must be at the bottom of the wheel.

So now when t = 0, we have:

[tex]\rm H(0) = 30ft\times cos(0 + \pi) + 38ft.\\\\\ H(0) = 8 \ ft.[/tex]

To learn more, about equations, refer;

https://brainly.com/question/10413253

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