# Thread: Finding a sine or cos function for a word problem question

1. ## Finding a sine or cos function for a word problem question

A spherical chocolate drops onto the top of a turning paddle wheel of radius 2.5m. The wheel rotates once every 3 seconds and its bottom is positioned at ground level.
a) How high is the chocolate after 1 second?
Since period = 3s, I think a equation for this scenario would be 2.5 cos (2pix)/3 +2.5. Then, the height would be 1.25m after 1 second. Is this correct?
b) The first time the chocolate reaches the bottom, it rolls off the paddle wheel with the same velocity it had when it traveled halfway around the wheel's circumference. It rolls to you, lying flat on the ground, with your mouth open, 5 meters away. Ignoring all friction, how long does it take for the chocolate to travel from the top of the paddle wheel to your mouth.

2. ## Re: Finding a sine or cos function for a word problem question

Part (a) is fine. I'd use $t$ for the independent variable instead of $x$ ... $h(t) = 2.5\cos(\omega t) + 2.5$

Part (b) ... $v=r\omega \implies d=r\omega t$