Let two particles collide. Particle 1 has initial velocity v, directed to the right, and particle 2 is initially stationary. 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 v1 and v2 of particles 1 and 2? Express answer in terms of the initial velocity, v. My conservation of energy equation for the two particles is (I already cancelled out the masses): v1^1 + 0.5v2^2 = v^2 My conservation of momentum equation is (masses already cancelled): 2v1 + v2 = 2v Thus, v2 = 2v-2v1 v1 = (2v-v2)/2 I tried plugging these values for v1 and v2 into the conservation of energy formula to try and isolate v for each variable. For v1, I ran into difficulty because of the middle term of the binomial equation, -8vv1. v1^1 + 0.5v2^2 = v^2 v1^2 + 0.5[(2v-2v1)(2v-2v1)] = v^2 v1^2 + 0.5[4v^2 - 8vv1 + 4v1^2] = v^2 -v^2 = v1^2 - 4vv1 + 2v1^2 3v1^2 - 4vv1 = -v^2 From here I spent like 10 lines trying to rearrange terms to separate v from that middle term (now -4vv1), but am unable to do so. Any ideas? Thanks!