A Ferris wheel seat

The question

Name: ______________________   Date: ____________   A Ferris wheel seat (6 points)

Graph

Height of a Ferris wheel seat

A Ferris wheel has a diameter of 40 meters, and its center is 25 meters above the ground. The wheel turns counterclockwise at a constant speed and completes one full turn every 8 minutes. At time $t = 0$ minutes, seat $S$ is at the lowest point of the wheel. The sinusoidal function $h$ models the height of seat $S$ above the ground, in meters, at time $t$. The graph of $h$ for one full turn is shown with its axes unscaled. The points $F$, $G$, $J$, $K$ and $M$ are on the graph: $F$, $J$ and $M$ are a lowest or highest point, and $G$ and $K$ are at the height of the center of the wheel.

1. (A) Find the coordinates of the points $F$, $G$, $J$, $K$ and $M$. [2 points]

2. (B) The function $h$ is given by $h(t)$$= a\sin(b(t + c)) + d$, where $a$, $b$, $c$ and $d$ are constants. Find values of $a$, $b$, $c$ and $d$. [2 points]

3. (C(i)) Is $h$ increasing or decreasing on the interval $(2, 4)$? Give a reason for your answer in the context of the problem. [1 point]

4. (C(ii)) Is the rate of change of $h$ increasing or decreasing on the interval $(2, 4)$? Explain your reasoning. [1 point]