Added to Six Flags St. Louis in the Colossus is a giant Ferris wheel. Its diameter is 165 feet, it rotates at a rate of about 1.6 revolutions per minute, and the bottom of the wheel is 15 feet above the ground. Determine an equation that relates a rider's height above the ground at time . Assume the passenger begins the ride at the bottom of the wheel.

The height of the rider as a function of time is , where time is measured in seconds.

Step-by-step explanation:

Given that Ferris wheel rotates at constant rate and rider begins at the bottom of the wheel, the height of the rider as a function of time is modelled after this expression:

Where:

- Height of the bottom with respect to ground, measured in feet.

- Angular speed of the ferris wheel, measured in radians per second.

- Time, measured in seconds.

- Radius of the Ferris wheel, measured in feet.

The angular speed of the ferris wheel, measured in radians per second, is obtained from the following expression:

Where:

- Angular speed of the ferris wheel, measured in revolutions per minute.

If , then:

Now, given that , and , the height of the rider as a function of time is:

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation: