Chapter 6.4, Problem 27PE

A Ferris wheel at a county Fair is $180\text{ ft}$ in diameter with its lowest point $2.5\text{ ft}$ off the ground. Once all the passengers have been loaded, the wheel makes one full rotation counterclockwise in $1.2\text{ min}$ . Suppose that two children are seated at the lowest point on the wheel and are the last passengers to be loaded when the wheel starts.

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

c. Give the coordinates of the children's position $1\text{ min}$ into the ride and describe the location.