Conservation Of Momentum

Total Momentum of the system is the Momentum of the centre of mass

ptotal = pcom= Mtotalvcom

The total momentum of a system is conserved if there are no external forces acting (e.g friction, gravity). 

This means that the momentum before a collision or explosion equals the momentum, 

pinitial  = pfinal

and since the total momentum of the system os the momentum of the centre of mass this means that;

pcom before  = pcom after

With no external forces acting this means that the velocity of the centre of mass must be CONSTANT as the total mass of the system doesn't change and  

pcom= mtotalvcom

Note: Not all collisions and explosions travel in a straight line and will often go off in many directions. Because of this we need to consider motion in both vertical (y) and horizontal (x) directions.