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)v_r = (40)(v_B)_x
(v_B)_x = 1.5(v_r)

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

Integrating with respect to time we have that:
2.5 s_r = (s_B/r)_x
2.5 s_r = (4/5)(30)
s_r = 9.6 m

So the distance travelled by the ramp is 9.6m