Question

a ferris wheel is 35 meters in diameter, and can be boarded at ground level. The wheel turns in a counterclockwise direction, completing one full revolution every 5 minutes. Suppose that at t=0 you are in the three o'clock position. Find a possible formula

Answer 1

Answer:

$y=17.5\sin\ \left(\frac{2\pi}{5}x\right)+17.5$

Step-by-step explanation:

Diameter of a ferris wheel is 35 meters and it can be boarded at ground level.

It means,

Maximum value = 35

Minimum value = 0

The general sine function is

$y=A\sin (Bx+C)+D$            .... (1)

where, A is altitude, $\frac{2\pi}{B}$ is period, C/B is phase shift and D is midline.

The wheel turns in a counterclockwise direction, completing one full revolution every 5 minutes.

$Amplitude=A=\frac{Maximum-Minimum}{2}\Rightarrow \frac{35-0}{2}=17.5$

Period = 5

$5=\frac{2\pi}{B}$

$B=\frac{2\pi}{5}$

$Midline=D=\frac{Maximum+Minimum}{2}\Rightarrow \frac{35+0}{2}=17.5$

At t=0 you are in the three o'clock position. It means the graph passes through the point (0,17.5), which lies on the midline. So, the phase shift is 0.

Substitute A=17.5, $B=\frac{2\pi}{5}$, C=0 and D=17.5 in equation (1).

$y=17.5\sin\ \left(\frac{2\pi}{5}x\right)+17.5$

Therefore, the required formula is $y=17.5\sin\ \left(\frac{2\pi}{5}x\right)+17.5$.