1. The problem statement, all variables and given/known data Hello! I am an honors physics student and i have been assigned a project that has puzzled me. I have a container full of sand, a couple meter sticks, a tennis ball, and a stopwatch. What I need to do is prove something through the use of these items. What I am going to try to do is prove that an object dropped from a taller height will create a bigger impact crater. This is a very elementary concept, I know. I just don't know how to mathematically relate the crater depth to the increase in energy. I see that with the height increase, the total energy increases. But how do I directly relate the crater depth to the energy increase? I can find the velocity before the impact, how do I factor in the velocity of the impact? 2. Relevant equations Ke=1/2MV2 Ep=MGH Vf2=Vi2+2AΔX 3. The attempt at a solution I am planning on conducting 25 drops: 5 from .5 meters, 5 from 1 meter, 5 from 1.5 meters, 5 from 2 meters, and 5 from 2.5 meters. With each height increase, I am expecting an increase in crater depth. I am just confused on how I am going to prove mathematically that the height increases crater size. I know that the combined energy before the impact will increase because Kenetic energy=1/2Mass * velocity2 (Ke=1/2MV2 ) and potential energy=Mass * Gravity * Height (Ep=MGH). The total energy would be the kenetic plus potential energy. As the height increases, the energy increases. Should there be a constant increase between the crater depth with each drop?