9. A Ferris wheel rotates in a clockwise direction and completes one rotation every 30 seconds. Point B is on the top of one of the enclosed carriers and is located directly above the center of the Ferris wheel at time \( t=0 \) seconds. Point B is 40 ft from the center of the Ferris wheel. Point C is exactly 40 feet east from the center of the Ferris wheel. The center of the Ferris wheel is 50 feet above the ground on which the Ferris wheel sits. As the Ferris wheel rotates at a constant speed, the distance between B and the ground periodically decreases and increases. a. Write a sine and cosine function that models Point B's height above the ground, in feet, as a function of time \( t \), in seconds. b. Write a sine and cosine function that models Point C's height above the ground, in feet, as a function of time \( t \), in seconds. c. On the interval \( [0,60] \), when is Point B increasing at the same time that Point C is decreasing? d. When \( t=15 \) seconds, what is the height off the ground of Point B and Point C? e. Does Point B or Point C have a greater rate of change on the interval \( [0,10] \) ? f. What is the minimum value of Point B / C? What does it represent in the context of the problem?
