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;

$d=30sin(\frac{\pi}{40}t)+20$

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

Step 2

Let the time for making one revolution be;

$T=\frac{2\pi}{\frac{\pi}{40}}=2\pi\times\frac{40}{\pi}=80seconds$

Note;

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

Answer;

$80\text{ seconds}$