1. The problem statement, all variables and given/known data (a.)Apply the law of conservation of momentum to the perfectly inelastic collision of a moving object of mass m1 and velocity vi with a stationary object of mass m2 (b.) Solve this for final velocity vf (c.) Write a formula for the initial kinetic energy (KEi) (d.) Write a formula for the final kinetic energy (KEf) in terms of vf (e.) Substitute your formula for vf from (a.) into your equation above to get a formula for KEf in terms of m1, m2, and vi alone (f.) Find the ratio KEf/KEi in terms of m1 and m2 alone (g.) Express the final kinetic energy in terms of the initial kinetic energy KEi (h.) For the case of a moving object much, much more massive than the stationary object (m1 >> m2), how much kinetic energy is lost in the collision? (i.) For the case of a stationary object much, much more massive than the moving object (m2 >> m1), how much kinetic energy is lost in the collision? (j.) Given two projectiles fired with the same KE, fired at a target which is free to move, which will cause the most destruction (that is, result in the greatest loss of kinetic energy), a small high-speed projectile or a massive slow-moving one? 2. Relevant equations Momentum: P = m x v Kinetic Energy: KE = 1/2mv^2 3. The attempt at a solution (a.) P = M1V1 + M2V2 = (M1+M2)Vf (b.) Vf = M1V1/(M1+M2) (c.) Cons. Energy, KEi = KE1 + KE2, KEi = 1/2(M1V1^2) + 1/2(M2V2^2) KEi = 1/2(M1V1^2) (d.) 1/2 (M1 + M2) Vf^2 (e.) Here's where my confusion starts, (M1+M2)Vf = M1V1 + M2V2 and 1/2(M1+M2)Vf^2, I tried 1/2(M1+M2)((M1V1+M2V2)/(M1+M2))^2, substituting in for Vf but I'm not sure if that's right (f.) I'm not even sure how to resolve this from the last piece of information, because I can't set M1 and M1 or M2 and M2 equal to each other from my previous formulas, can I? Since I'm stuck there I couldn't make an attempt on the rest yet.