Question

A Ferris wheel has a diamerter of 50 meters and makes one revolution every 15 minutes. The loading dock is 5 meters off the ground. At time zero you are at 3 o'clock going down. Find the height above ground as a function of time and provide a graph.

Answer 1

Thus, the max height of the graph is 50 + 5 = 55m

Since the graph complete revolution in 15 minutes, which is ( 15 x 60 =900 seconds )

Thus, the periodic graph we look like this

Given the sine graph equation

$\begin{gathered} y=a\sin (bx-c)+d \\ a\Rightarrow amplitude \\ a=\frac{55-5}{2}=\frac{50}{2}=25 \\ d=\frac{55+5}{2}=\frac{60}{2}=30\Rightarrow\text{midpoint} \\ b=\frac{2\pi}{15} \\ c=\frac{15}{4}=3.75 \end{gathered}$

Hence the equation of the height above the ground as a function of it is

$\begin{gathered} h=y \\ t=x \\ h=a\sin (bt-c)+d \\ h=25\sin (\frac{2\pi t}{15}-\frac{15}{4})+30 \end{gathered}$

The graph is