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=(55-5)/(2)=(50)/(2)=25 \\ d=(55+5)/(2)=(60)/(2)=30\Rightarrow\text{midpoint} \\ b=(2\pi)/(15) \\ c=(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 ((2\pi t)/(15)-(15)/(4))+30 \end{gathered}`

The graph is