At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 50 meters and a diameter of 35 meters. It takes the wheel 11 minutes to make one revolution. Write the sinusoidal function, f(t), that models the height of your chair at any time, t.

Question

anonymous · Answer

Sinusoidal function...
$$f(t) = A \sin \omega t$$

anonymous · Answer

A can be determined from "maximum height of 50 meters and a diameter of 35 meters"...
maximum height = 50 meter
minimum height = 50-35 = 15 meter
therefore what is A?

anonymous · Answer

One revolution = 11 minutes, this is equivalent to 1 period of a sine wave, from 50 meters then 15 meters then return to 50 meters again...

anonymous · Answer

from the information above, we can complete the sinusoidal function... :)

anonymous · Answer

... just the same as the simple harmonic motion we have previously (on your last problem)...

deadshot · Answer

so then it's $$f(t)=11\sin(\frac{ 2\pi }{ 35 })t+50$$?

anonymous · Answer

no...
we said that for A, it is the amplitude of the function that varies from maximum to minimum... in your problem what quantity varies from maximum to minimum?

deadshot · Answer

the height of the chair

deadshot · Answer

so then would it be $$f(t)=17.5\sin(\frac{ 2\pi }{ 11 })t+15$$ ?

anonymous · Answer

|dw:1384433782475:dw|

deadshot · Answer

The only options for amplitude on my homework are 11 and 17.5

anonymous · Answer

yes... that's correct... half of wheel diameter... and time t must be in minutes also....

deadshot · Answer

Alright, Thanks!