There is a faucet dripping water from height $H$ onto a smooth, horizontal ceramic surface, and I need to give a upper bound of the maximum distance between the water spatter and the point directly below the faucet. The naive estimate would be to think a single water drop as a bouncy ball, which on collision changes direction while maintaining its magnitude of momentum (somehow). With this assumption the maximum distance $h=H/2$. But I don't think this assumption is good enough, because water drops will break up by impact, and the momentum might be distributed unevenly, causing the smaller parts to be faster than its original velocity.
So is there any other better model for this problem? I did a quick Google search on the topic, and it seems that there are some forensics study on blood spatter, but they don't really match this scenario. And I kind of secretly hope that the viscosity of water don't play a major part in this problem (it's water, not honey, right)