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

f(t)=30sin pi/15 t+25

Explanation:

I did the diagnostic :)

Answer 2

The required function is
`h(T)=30\sin ((\pi T)/(15))+25`.

Explanation:

The general sine function is

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

Where, A is amplitude,
`(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=(Maximum+Minimum)/(2)=(55+5)/(2)=30`

The Midline of the function is

`D=(Maximum-Minimum)/(2)=(55-5)/(2)=25`

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

`(2\pi)/(B)=30\Rightarrow B=(2\pi)/(30)=(\pi)/(15)`

`2\pi=30B`

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

`y=30\sin ((\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 ((\pi)/(15)T+0)+25`

Therefore the required function is
`h(T)=30\sin ((\pi T)/(15))+25`.