Write an Equation about the Movement of a Ferris Wheel

Question

^{The lowest point of a ferris wheel is 20 feet above the ground and the wheel has a radius of 35 feet. The ferris wheel goes around every 2 minutes. Find an equation for the distance with respect to a point on the ground.}

Answer 1

Well, we have a cosine graph. Since it's 20 feet off the ground, the middle is 35 + 20 = 55 feet off the ground.

y = cos(x) + 55

The regular period is 2π, so...

2 = 2π/B

2B = 2π

B = π

y = cos(πx) + 55

Answer 2

A ferris wheel that starts at its lowest point of 20 ft above the ground can be modeled by a sin curve.

The general equation for a sin curve is y = a sin b(x+c)+d

a is the amplitude. In this case the amplitude is the radius of the ferris wheel, 35.

to find b, 2π/b = frequency. Since it takes 2 mins for one revolution.

2π/b = 2

Solving this equation, b=π

c is the horizontal shift. There is no horizontal shift in this problem

d is the vertical shift. This is 35+20 (The radius of the ferris wheel + how far it is off the ground. d=55.

Plugging all this into the equation:

y = 35 sin (πx)+55