To find the velocity of the center of mass before and after the collision, we first need to calculate the initial momentum and the final momentum of the system. We can then use the conservation of momentum and the definition of the center of mass to calculate its velocity. 1. Calculate the initial momentum: The initial momentum of the system is given by the sum of the momenta of the two balls before the collision. p_i = m_1 * v_1 + m_2 * v_2 where, m_1 = 0.200 kg (mass of first ball) v_1 = 150 m/s (velocity of first ball) m_2 = 0.300 kg (mass of second ball) v_2 = -0.4 m/s (velocity of second ball, negative because it is moving in the opposite direction) p_i = (0.200 kg)(150 m/s) + (0.300 kg)(-0.4 m/s) p_i = 30 - 0.12 p_i = 29.88 kg m/s 2.Calculate the final momentum: Since the collision is elastic, the total momentum of the system is conserved. Therefore, the final momentum of the system is equal to the initial momentum. p_f = p_i = 29.88 kg m/s 3.Calculate the velocity of the center of mass before the collision: The center of mass is defined as the weighted average of the positions of the particles, where the weights are the masses of the particles. Since the balls are moving in opposite directions, the center of mass is located somewhere between them. However, since the problem does not give us any information about the positions of the balls, we will assume that they are initially at rest and that the center of mass is located at the midpoint between them. r_cm = (m_1 * r_1 + m_2 * r_2) / (m_1 + m_2) where, r_1 = 0 m (position of first ball) r_2 = -d (position of second ball, where d is the distance between the balls) d = (m_1 + m_2) / 2 = 0.250 kg (distance between the balls, assuming they are initially at rest) r_cm = (0.200 kg * 0 m + 0.300 kg * (-0.250 m)) / (0.200 kg + 0.300 kg) r_cm = -0.075 m The velocity of the center of mass before the collision is then given by: v_cm,i = (m_1 * v_1 + m_2 * v_2) / (m_1 + m_2) v_cm,i = (0.200 kg * 150 m/s + 0.300 kg * (-0.4 m/s)) / (0.200 kg + 0.300 kg) v_cm,i = 29.7 m/s Therefore, the velocity of the center of mass before the collision is 29.7 m/s. 4.Calculate the velocity of the center of mass after the collision: The final velocity of the center of mass can be calculated using the conservation of momentum and the definition of the center of mass. p_f = m_total * v_cm,f where, m_total = m_1 + m_2 = 0.500 kg (total mass of the system) v_cm,f = final velocity of the center of mass v_cm,f = p_f / m_total v_cm,f = p_i / m_total (since p_f = p_i) v_cm,f = 29.88 kg m/s / 0.