Answer
$y=11-10cos(\frac{\pi}{10}t)$ with t=0 at lowest point.
Work Step by Step
Step 1. Identify the quantities as $r=10m, h_0=1m, p=20s$ where $h_0$ is the lowest height.
Step 2. Assume the person starts at the lowest height, use a cosince function to model the height of the person on the Ferris wheel as $y=h_0+r-r\cdot cos(\omega t)$. With $p=\frac{2\pi}{\omega}=20,\omega=\frac{\pi}{10}$, we have $y=1+10-10cos\frac{\pi}{10}t$ or $y=11-10cos(\frac{\pi}{10}t)$
Step 3. Check the correctness of the equation: at $t=0s$, the wheel is at its lowest point $y=1$, at $t=10s$ the wheel is at its highest point $y=21$
Note: the answer in the book used a sine function which assumed that the person was at a height of 11m at t=0.
