A 40 kg rectangular crate is placed on at the top of a triangular ramp as shown in the figure. The rectangular crate is starting from rest at the point A and the 60 kg ramp is free to roll. Determine the distance the ramp moves when the crate slides 30 m down the ramp and reaches the bottom B.

1) 9.6m
2) 5.5m
3) 8.7m
4) 4.8m

The equation of momentum can be written as
S mv1 = S mv2
0 = (60)vr = (40)(vB)x
(vB)x = 1.5(vr)

Also vB = vr + vB/r and if we consider that the movement of the ramp is positive then we have the equation as:
-(vB)x = vr - (vB/r)x
-1.5vr = vr - (vB/r)x
(vB/r)x = 2.5 vr

Integrating with respect to time we have that:
2.5 sr = (sB/r)x
2.5 sr = (4/5)(30)
sr = 9.6 m

So the distance travelled by the ramp is 9.6m