A body of mass 12kg traveling at 4.2ms-1 collides with a second body of mass 18kg at rest. Calculate their common velocity if the two bodies coalesce after ...

A body of mass 12kg traveling at 4.2ms-1 collides with a second body of mass 18kg at rest. Calculate their common velocity if the two bodies coalesce after collision

Answer Details

The conservation of momentum states that the total momentum of a system of objects remains constant if there are no external forces acting on the system. In this problem, we can use this principle to determine the common velocity of the two bodies after the collision. Before the collision, only the 12 kg body is moving, so the total momentum of the system is: 12 kg x 4.2 m/s = 50.4 kg m/s After the collision, the two bodies move together with a common velocity v. Since they stick together, their final mass is 12 kg + 18 kg = 30 kg. Therefore, the total momentum of the system after the collision is: 30 kg x v = 50.4 kg m/s Solving for v, we get: v = 50.4 kg m/s / 30 kg = 1.68 m/s So the common velocity of the two bodies after the collision is 1.68 m/s, which is closest to option D, 1.7 m/s.