I have been doing an experiment about relationship between drop height of a stone and the loss of water in the cup it lands in. I found that after dropping the same stone into a cup with the same mass/volume of water that it gave a straight line (positive gradient) graph. I need to include the principles behind this but I am unsure... Is it because of the differing or same velocity that it hits the water at? or the energy the stone has?
It is because stones dropped from a larger height have reached larger speeds when touching the water and larger speeds means more kinetic energy and momentum, and that means a larger explosion, and that means more water falling out of the cup. Every nonlinearity in some level is cancelled by another one at another level such that the relationship between height and water spilled is linear.