Help me with this sliding object and velocity ptoblem?

Question

A sledge of 100kg is sliding across the ice and a package of 25 kg is dropped vertically on the sledge. What is the ratio of the final KE of the sledge with package to the initial KE of the sledge before package was dropped? Friction can be neglected I feel. Please answer with the explanation.

Answer 1

momentum of horizontal motion will be conserved.  The package has no momentum in the horizontal plane.  Therefore the sledge slows down in proportion to its increase in mass.  Its velocity drops to 100/125 = 0.8 of its initial value.  The new KE is therefore factored up by the increased mass and down by the decreased velocity squared to give 1.25 x 0.8 x 0.8 = 0.8