You are riding the ferris wheel at the Montgomery County Fair. The wheel has a diameter of 36 feet and travels at a constant rate of 3 revolutions per minute. A car at its lowest is 4 feet above the ground. Write a sine function to describe the relationship between time and the height of the car above the ground. State the period, phase shift, vertical shift, and amplitude of the equation.

Question

(i do not understand this question at all, sorry if there isn't any work done)

Answer 1

If you understand since functions, you must understand this. The height of a point on a rotating circle is ha sine (or cosine) function.

The question does not state at what point to start measuring, so we will start with the car at its lowest point at t=0.

Since cos(t) is a max at t=0, we will need to use

h = -Acos(t)

where A is the amplitude. Since the wheel has a diameter of 36, it varies above and below the axle by haf that, or 18.

h = -18cos(t)

But, the car at its lowest is at +4, and not -18, so we need to shift the curve up by 22.

h = 22 - 18cos(t)

But, cos(t) has a period of 2π. cos(kt) has a period of 2π/k. We want a period of 1/3 (3 rpm is the frequency, which is the reciprocal of the period.) So,

2π/k = 1/3 --> k = 6π

h = 22 - 18cos(6πt)

Hmmm. The questions asks for a sine function. Since sin(x) = cos(π/2-x), we finally come to the function

h(t) = 22 - 18sin(π/2 - 6πx)
or
h(t) = 22 + 18sin(6π(x - 1/12))

If you check the graph linked below, you will see indeed that
the amplitude is 18
the period is 1/3
the phase shift is 1/12

http://www.wolframalpha.com/input/?i=y+%3D+22+%2B+18sin%286%CF%80%28x-1%2F12%29%29%2C+y%3D40%2C+y%3D4