Originally Posted by toly
No, it can be and must be the same. It is the absolute truth.
There are zillions of articles in which authors use this well known fact. See for instance citation from article, “Elastic and Inelastic Collision in Two Dimensions”, http://www.plasmaphysics.org.uk/collision2d.htm
"For the sake of simplicity it has been assumed here that mass 2 is initially resting i.e. vx,2=0, vy,2=0 and vx,2'=Δvx,2' (this does not affect the general validity of the final result as the assumption will be dropped again later by referring the velocities to mass 2 explicitly)."
Don’t try to invent new physics please.
Mass 2 is resting sets one of the variables to 0. That is not what you are saying. You are saying relative velocities are all that matter. That is like replacing vx1 by vx1-vx2.
Say you have a small mass m moving horizontally to the right with speed v and colliding completely inelastically with a larger mass M. The two together will then move to the right with speed mv/(m+M). If m was stationary and M moved to the left with speed v, the two will move to the left with speed Mv/(m+M).