I given to objects of masses m1 and m2 and initial velocities v1 and v2, I know how to find out out v1' and v2', their velocities after the collision by settings up simultaneous equations. However, that takes a long time to solve, and there is a shortcut that my teacher told my class that I wrote down on a sheet of paper but then lost. I tried searching Google and haven't gotten any luck yet. I remember the shortcut was something like: v1'=2((m1v1+m2v2)/(m1+m2))-v1 v2'=2((m1v1+m2v2)/(m1+m2))-v2 But I'm not sure. Would anybody know what the shortcut is?