Originally Posted by sureshs
It cannot be the same.
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.