Question

The distance from the ground of a person riding on a Ferris wheel can be modeled by the equation d=30sin(pi/40t)+20, where d represents the distance, in feet, of the person above the ground after t seconds. How long will it take for the Ferris wheel to make one revolution?30 seconds40 seconds80 seconds20 seconds

Answer 1

Step 1

Given;

`d=30sin((\pi)/(40)t)+20`

Required; How long will it take for the Ferris wheel to make one revolution

Step 2

Let the time for making one revolution be;

`T=(2\pi)/((\pi)/(40))=2\pi*(40)/(\pi)=80seconds`

Note;

`\begin{gathered} For\text{ a trigonometric function} \\ f(x)=asin(wt)+b \\ T=(2\pi)/(w) \end{gathered}`
`\begin{gathered} T\text{ is the period for one revolution} \\ w=(\pi)/(40) \end{gathered}`

Answer;

`80\text{ seconds}`