The teacher screwed up and gave us a problem that he could not solve.
I am trying to solve it for fun.
A roller coaster has a cosine shape.
The coaster starts at the top (0 pi) with near 0 velocity
Friction is 0, and there is no air resistance.
Want a hint... Not a full solution
The Attempt at a Solution
Tried to integrate vdv = sin(theta)d(theta) from 0 to pi/2
Answer = 0 (doh!) Should have seen that before I started!
Teacher conjectures that the result will be the same as if the coaster went down a straight ramp at 45 degrees, but can't prove it. It is bugging him too.
Thanks in advance,