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A small block is released from rest on a movable wedge; every contact surface is frictionless and the system is just the wedge plus block(s). Considering the motion until the block reaches its maximum height on the wedge, which statement is correct?

1. At the maximum height, the block and the wedge move with a common velocity.
2. The acceleration of the centre of mass of the system is first vertically downward and then vertically upward.
3. The centre of mass of the system has a horizontal acceleration toward the wedge's motion.
4. The block and wedge always move with equal and opposite accelerations of the same magnitude.

Correct answer: At the maximum height, the block and the wedge move with a common velocity.

Solution

With no external horizontal force the centre of mass has no horizontal acceleration; at maximum height the block's velocity relative to the wedge vanishes, so block and wedge share a common (here zero horizontal) velocity at that instant.

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