Chapter 1.2, Problem 2E

Exercise 2 Conservation of Linear Momentum Is Covariant Under the Galilean Transformation. Assume that two masses ${m^{\prime }}_1$ and ${m^{\prime }}_2$ are moving in the positive x direction with velocities ${v^{\prime }}_1$ and ${v^{\prime }}_2$ as measured by an observer in ${\text{S}}^{\prime }$ before a collision. After the collision, the two masses stick together and move with a velocity $v^{\prime }$ in ${\text{S}}^{\prime }$. Show that if an observer in ${\text{S}}^{\prime }$ finds momentum to be conserved, so does an observer in S.