The velocity of the center of mass before the collision can be calculated using the following formula: v_cm = (m1v1 + m2v2) / (m1 + m2) where m1 and v1 are the mass and velocity of ball 1, and m2 and v2 are the mass and velocity of ball 2. Substituting the given values, we get: v_cm = (0.200 kg x 150 m/s + 0.300 kg x (-0.4 m/s)) / (0.200 kg + 0.300 kg) v_cm = (30 - 0.12) / 0.5 v_cm = 59.76 m/s Therefore, the velocity of the center of mass before the collision is 59.76 m/s. The velocity of the center of mass after the collision can be calculated using the following formula: v_cm’ = (m1v1’ + m2v2’) / (m1 + m2) where v1’ and v2’ are the velocities of ball 1 and ball 2 after the collision. Since this is an elastic collision, we know that momentum is conserved: m1v1 + m2v2 = m1v1’ + m2v2’ Substituting the given values, we get: 0.200 kg x 150 m/s + 0.300 kg x (-0.4 m/s) = 0.200 kg x v1’ + 0.300 kg x v2’ Solving for v1’ and v2’, we get: v1’ = (-0.3 / 0.2) x (-0.4 - 59.76) = 89.64 m/s v2’ = (0.2 / 0.3) x (150 - 59.76) = 90.16 m/s Therefore, the velocity of the center of mass after the collision is 89.9 m/s. I hope this helps! Let me know if you have any other questions.