You have been assigned the task of designing a new Ferris wheel for Six Flags! The design has to be completed and approved before
construction can begin.

1) Sketch the ferris wheel (remember the wheel can't touch the ground). Mark the height from the ground, the radius of the wheel, and the total
height of the ride.

2) Determine the radius of your wheel. What is the distance traveled in one revolution of the Ferris wheel (arc length)?

3) If the wheel is modeled as a clock, what is the distance of the rider from the ground at 12:00, 3:00, 6:00, and 9:00? Mark it in the table below.
Assume the rider gets on the ride when the car is at 6:00 or 0 seconds. Assign a speed to the wheel (How long does it take to make one revolution?
If it takes x seconds to make one revolution, then each position is 1/4 of the time or x/4 seconds)

Postion Height Time in seconds

6:00 0
9:00
12:00
3:00
6:00
9:00
12:00
3:00
6:00

4) The height of a rider on a Ferris wheel can be modeled by an upside-down cosine curve. Think about what is the midline for your curve (on the Ferris
wheel, what is the amplitude, and how long does it take to do one revolution (this is the period). Write the equation to model your Ferris wheel,
where y is the height of the rider and x is the time the rider is in the air.

y = ___ cos(x) + ___