1. The problem statement, all variables and given/known data Prove kinetic energy is relationship between mass and velocity using E(g)=mgh (no calculus, momentum, kinematics). 2. Relevant equations gravitational energy: E=mgh kinetic energy: E=(1/2)mv^2 3. The attempt at a solution I know it can be derived using the gravitational energy equation (E=mgh) and the kinematic equation (Δv^2)=2aΔx. If I'm correct, conservation of energy (in free fall situation) states that E gravitational before being dropped = E kinetic when object hits the ground. I've been led to believe that I can prove the kinetic energy formula only needing E(g)=mgh and E(g)=E(k). This does not seem like enough information though. I'm stuck trying to prove that height doesn't affect kinetic energy and that the relationship between mass and velocity is (1/2) and ^2. Am I wrong that kinetic energy can be derived only knowing E(g)=mgh and E(g)=E(k)?