A ball of mass m and a ball of unknown mass M approach each other from opposite directions and have the same speed Vo (but oppositely directed velocities). The ball of M is reduced to rest by the impact, while the ball of mass m has a velocity V1'. What are the ratios a) M / m b) V1' / Vo This is what I've done so far. I ended up with 2 answers, but we're only supposed to have one. Conservation of momentum: mVo + M(-Vo) = mV1' + 0 - divide both sides by mVo, and let x = M / m, y = V1' / Vo ... equation (1'): 1 - x = y Conservation of kinetic energy: 1/2mVo^2 + 1/2M(-Vo)^2 = 1/2mV1'^2 - divide both sides by 1/2mVo^2 ... equation (2'): 1 + x = y^2 equations (1') + (2'): y^2 + y - 2 = 0 (y + 2)(y - 1) = 0 ... y = -2 or 1 Case 1: If y = -2, x = 3 Case 2: If y = 1, x = 0 I dont know how we're supposed to determine which is the correct case. Please help!