Chapter 6, Problem 50RE

A Ferris wheel is $200\text{ ft}$ in diameter with its lowest point $3\text{ ft}$ off the ground. Once all the passengers have been loaded, the wheel makes one full rotation counterclockwise in $3\text{ min}$ . Suppose that a couple is seated at the lowest point on the wheel and are the last passengersr to be loaded.

a. Write a model representing the couple's horizontal position $x$ (in feet) relative to the center of the Ferris wheel, $t$ minutes after the ride starts.

b. Write a model representing the couple's height $y$ (in feet) above ground level, $t$ minutes after the ride starts.

c. Give the coordinates of the couple's position $2\text{ min}$ into the ride and describe the position.