Linear momentum question HELP ASAP

Question

A 10-g bullet moving directly upward at 500 m/s hits and passes through the centre of mass of a 4-kg block initially at rest, as shown in the figure. The bullet emerges from the block moving directly upward at 100 m/s. Assume that the bullet passes through the block very quickly. Determine: a) (5 marks) The speed of the block immediately after the bullet exits. b) (5 marks) The maximum height the block rises above its initial position. Take g = 10 m/s^2. Show your detailed work.

So I found A to be 1m/s which is correct. For the second one I used delta kinetic energy + delta potential energy=0 and I got -0.05m as the height. The answer is supposed to be positive 0.05m. Why doesn't this equation work?

Answer 1

If you choose the zero level for the gravitational energy as the initial position of the block right before and after the collision; then you'd have only kinetic energy after the collision, which goes into gravitational energy as the block reaches its maximum height h. So, you'd have 1/2 M v^2 = M g h, which you would solve for h.

Your approach also works. U_i + K_i = Uf + K_f, so ΔK + ΔU = 0.

ΔU = Mgh - 0 = Mgh;

ΔK = 0 - 1/2 Mv^2 (because the block is at reach at its maximum height).

So you'd have Mgh - 1/2Mv^2 = 0, which gives us again a positive maximum height.