1. The problem statement, all variables and given/known data The question I have is not how to arrive at the correct values of final velocity, but once I have the values of final velocity, how do I know which velocities (which are computed from a quadratic equation) are correct? Two blocks, block A and Block B, are travelling to the right. Before collision: Block A is 4kg at 10m/s Block B is 2kg at 5m/s After collision: Block A is 4kg at vf = ? Block B is 2kg at Vf = ? Energy loss is .05 2. Relevant equations mvi + MVi = mvf + MVf 1/2mvf^2 + 1/2MVf^2 = .95[1/2mvi^2 + 1/2MVi^2] 3. The attempt at a solution mvi + MVi = mvf + MVf ==> Vf = 25 - 2vf 1/2mvf^2 + 1/2MVf^2 = .95[1/2mvi^2 + 1/2MVi^2] ==> 4vf^2 + 2Vf^2 = 427.5 4vf^2 + 2(25 - 2vf) = 427.5 ==> 12vf^2 - 200vf + 822.5 = 0 Quadratic Formula ==> vf = 9.28m/s and 7.38m/s then, Vf = 25 - 2(9.28) = 6.44m/s and Vf = 25 - 2(7.38) = 10.24m/s So the possible answers are: [vf = 9.28m/s Vf = 6.44m/s] or [vf = 7.38m/s Vf = 10.24] Given the energy loss of .05, how could I know which set of final velocities are correct? I don't think I can just rationalize it because in either case, the faster, heavier block A slows down upon colliding with the lighter, slower block B. And Block B speeds up upon being struck by the faster, heavier block A. What I mean is, in both final answers, Block A is slowing down and Block B is speeding up. Is there a computation that will determine which set of velocities are correct?