1. The problem statement, all variables and given/known data Let two particles of equal mass m collide. Particle 1 has initial velocity v, directed to the right, and particle 2 is initially stationary. A: If the collision is elastic, what are the final velocities v_1 and v_2 of particles 1 and 2? B: Now assume that the mass of particle 1 is 2m, while the mass of particle 2 remains m. If the collision is elastic, what are the final velocities v_1 and v_2 of particles 1 and 2? 2. Relevant equations i: mv_1 + mv_2 = mv ii: 0.5m(v_1)^2 + 0.5m(v_2)^2 = 0.5mv^2 iii: 2mv_1 + mv_2 = 2mv iv: 0.5(2m)(v_1)^2 + 0.5m(v_2)^2 = 0.5(2m)v^2 3. The attempt at a solution For A, after factoring out m and rearranging equation i to solve for v_2 I replaced v_2 in equation i with v_2 = (v - v_1) to yield: v_1 + v_2 = v_1 + (v - v_1) = v_1 - v_1 + v = v, therefore v = v. I guessed (correctly) that v_1 = 0 and v_2 = v, but I'm not sure how I can find those answers using this equation. It's the same thing with part B. I tried rearranging the kinetic energy equations ii and iv for both parts A and B but still came out with such useless results as v^2 = v^2. Why does particle 1 in part A transfer all of its momentum to particle 2?