I said "relative velocities" because that's what you have to use to figure out what the ABSOLUTE velocity of the crate is.
v.crate.x = v.crate*cos(theta) - v.ramp
you have to subtract out the velocity of the ramp relative to the crate.
Ultimately I'm using the absolute velocities of...
E1 = E2
The apple is still moving at the top of the arc, so there's still some kinetic energy left over.
KE1 = KE2 + PE2
(1/2) * m * (v1)^2 = (1/2)*m*(v2)^2 + m*g*h2
At the peak of the arc, there is no y-component of velocity. All that's left at the top is the x-component. Since...
I used the correct value for g, I just used more decimal places than just 9.81. It's really 9.80665, but typically rounded to 9.81.
I didn't use the English g in ft/s^2 because I prefer to work in the metric system.
Ultimately it doesn't matter which system you use as long as you stay...
nocturnus,
I have worked this problem before. It was a test question when I was in dynamics.
I made a youtube video about how to solve it.
I hope this helps.
http://www.alexpleasehelp.com/online/problems/rollingramp