Original: Thus , when a gun is fired , the final total momentum of the system ( the gun and the bullet ) is the vector sum of the momenta of these two objects . Assuming that the gun and bullet were at rest prior to firing ( meaning the initial momentum of the system was zero ) , the final total momentum must also equal 0 .
Simplified: Using vector addition to add the momentum of the bullet to the momentum of the gun ( equal in size but opposite in direction ) gives a total system momentum of zero .