Cart OH has a mass 2M and is released from rest at a height 4H on a ramp making an angle 2 with the horizontal, as shown above. Cart OE has mass 4M and is released from rest at a height 2H on a ramp making an angle with the horizontal. The carts roll towards one another, experience a head-on collision on the level/horizontal portion of the ramp, and lock together. The masses of the carts’ wheels, as well as any frictional and drag forces, will be considered negligible. Derive an algebraic expression for the velocity of the locked carts after the collision in terms of the variables in the prompt and the gravitational constant.