sinusoidal motion

[sxk1693]

It has been a break full of disappointment, but finally I have something to be happy about. A 330 on a math test! My previous high was like a 290.

Anyways, the only problem I skipped:

A carnival ferris wheel is 52 feet in diameter and turns at 6RPM. The bottom of the ferris wheel is 3ft. above the ground. The height varies sinusoidally with time. How high is the person after 3 seconds?
My equation was [unparseable or potentially dangerous latex formula] .
This keeps giving me 45 but the answer is 37.
Any suggestions?
Is it because I don't have a phase shift?

[nsguy1350]

The amplitude should be 26 (think: radius), and the vertical shift should be 29 (the baseline [line that divides the wave into an upper and lower half] of the sine wave is normally at the x-axis, but here it's 29 feet in the air.)
6RPM = 1 rotation every 10 seconds, or the period is 10 seconds. The sine wave has equation [unparseable or potentially dangerous latex formula] where [unparseable or potentially dangerous latex formula]. Therefore, [unparseable or potentially dangerous latex formula]. We already know [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula]

I assume the "person" starts at the bottom. The sine wave generally has a value of it's baseline at [unparseable or potentially dangerous latex formula]. Here, at [unparseable or potentially dangerous latex formula], the sine wave has its lowest possible value, or the value of its trough. That is a rightward shift equal to [unparseable or potentially dangerous latex formula] of its period, so [unparseable or potentially dangerous latex formula]. Thus the equation is [unparseable or potentially dangerous latex formula]. This gives [unparseable or potentially dangerous latex formula]

Hope that helps!

[101dalmatians]