Interesting physics problem about a bullet piercing through an object

Question

A cube made of foam with mass of 100g is placed on a weak horizontal surface. The height of the cube is 10 cm. Then, a person shoots a bullet underneath the cube. The initial velocity of the bullet entering the cube is 100 m/s, after exiting the cube - 95 m/s.

Will the cube move up? If yes, what is the maximum height?

Answer 1

Conservation of momentum ... 10*100=10*95+100v_b thus v_b=0.5 m/s. The energy of the block =.5mv² and will result in a height of mgh ... Solve for h = .25/2g=.0127m