A plate of mass $M$ moves horizontally with initial speed $v$ on a frictionless table. An object of mass $m$ is dropped vertically onto it from the height $h$ and smashes. How much energy is dissipated in this process?
I have been taught E-L formulas, but don't see how they could be applied to the question at hand.
In the y direction, the falling object gains energy due to gravitational potential and eventually smashes on the plate. Since the table is frictionless, I imagine that energy in the x-direction would be conserved. Thus, I first imagined that the dissipated energy came only from mgh. Of course, this answer doesn't make use of the E-L formula and I was told that I am overlooking something.
I have absolutely no idea how to approach this and hate to be so vague, but I'm at a complete loss. Any push in the right direction would be appreciated!