Perfectly elastic collisions problems usually involve calculating the final velocities of two masses from their initial momenta. Trying to derive such formula I got a different result, a shorter formula to solve the same problem: Take two masses a and b with their respective initial volocities; First I assumed the velocity of the center of mass to be constant; vc=const. Then I moved my referential to the mass a. In this referential I assumed that the absolute value of the relative velocites between the mass a and the center of mass to be also constant. What I imagined what more or less like this: Before the collision I would see the center of mass move towards my referential with a velocity "via-vc". After the collision I would see the center of mass move in the opposite direction with the same speed; Based on this what I got was: |via-vc|=|vfa-vc|=const. via-vc=vc-vfa via+vfa=2*vc That's it. The oddity is that it uses a rather faster thought, works perfectly and I've never seen before. Now you can solve collisions problems with a quicker equation :) Did you knew about this equation? Tell me what you think.