Math Ferris Wheel Problem

Question

A mini Ferris wheel has a radius of 5 inches and its center is 6.5 inches above the ground. It turns once every 30 seconds. To the nearest tenth of an inch, what is the height of a point on this Ferris wheel at the 8'o clock position?

Answer 1

The answer could be in the form h = a * cos θ +b.

Let the angle be measured counterclockwise from the line going from the center of the wheel to the bottommost position of the wheel.

In this case, h = a * cos(0) + b

1.5 = a * 1 + b Solve for b to get b = 1.5 - a

When the wheel has turned 180 degrees, the equation becomes

11.5 = a* cos180 +b

11.5 = -1*a +b Now substitute b = 1.5 - a

11.5 = -a + 1.5 -a

11.5 -2a +1.5 or a = -5

b = 1.5 - (-5) = 6.5

So, the final equation is h = -5 cos θ + 6.5

At 8 o'clock θ = 10/12 x 360 = 300 degrees (8 o'clock is 10/12 of 360 degrees, counting CCW.

h = -5*cos(300) + 6.5 = 4 inches