For collisions in two dimensions, the conservation of momentum is true for each component. That is,
PTot,i = PTot,f
is really a vector equation and means
PTot,i,x = PTot,f,x
PTot,i,y = PTot,f,y
For an inelastic collision, these provide two equations so we can solve for two unknowns. Usually this will be the final speed and the direction (or angle) of the final velocity of the two masses that are now stuck together.
For an elastic collision we have three equations for the Kinetic Energy is also conserved,
Ki = Kf
so now we can solve for three unknowns. This can mean two final speeds and one direction (that is, we must "know" the other direction to solve for the two final speeds and the "other" direction). Or it can mean that we can solve for one final speed and the two final directions (we will need the "other" final speed in order to solve for these three unknowns).
1D Collisions Center of Mass Return to ToC, Ch9, Linear Momentum (c) Doug Davis, 2001; all rights reserved