Wave created on water due to object impact

Let a spherical object of mass ? and volume ? be dropped in water from height ℎ, with an energy E and ? be the amplitude of the wave generated. What is the relation between ? and E. I know the proportionality between energy and amplitude is A^2 proportional to E. But I am looking for a specific equation that shows this relation. I also want to know the physics behind this process of an object impacting the water surface creating waves.

I am thinking of conducting an experiment for my IB Physics EE on this topic by dropping a sphere ball into a water tank and measuring the amplitude of the wave created. But I have a feeling that this experiment and exploring the relation between Energy and Amplitude is too simple. So it will be great if someone can give me good tips on possible modifications I can make to my experiment or topic to make my EE.