Question

a ferris wheel rotates around in 30 seconds. the maximum height above theground is 55 feet and the minumum height above the ground is 5 feet. what function would model the height as a funtion of T in seconds

Answer 1

55 times 30 is 1650 and 30 times 5 is 150
The answer is 1650 over 150

Answer 2

Answer:

The required function is $h(T)=30\sin (\frac{\pi T}{15})+25$.

Step-by-step explanation:

The general sine function is

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

Where, A is amplitude, $\frac{2\pi}{B}$ is period, C is phase shift and D is midline.

It is given that the maximum height above the ground is 55 feet and the minimum height above the ground is 5 feet.

The amplitude of the function is

$A=\frac{Maximum+Minimum}{2}=\frac{55+5}{2}=30$

The Midline of the function is

$D=\frac{Maximum-Minimum}{2}=\frac{55-5}{2}=25$

A ferris wheel rotates around in 30 seconds. So, the period of the function is 30.

$\frac{2\pi}{B}=30\Rightarrow B=\frac{2\pi}{30}=\frac{\pi}{15}$

$2\pi=30B$

Substitute A=30, $B=\frac{\pi}{15}$, C=0 and D=25 in equation (1), to find the required function.

$y=30\sin (\frac{\pi}{15}x+0)+25$

The required variable is T. Replace the variable x by T. So the height function is

$h(T)=30\sin (\frac{\pi}{15}T+0)+25$

Therefore the required function is $h(T)=30\sin (\frac{\pi T}{15})+25$.