I worked on the momentum problem and this textbook teaches most things in the cm frame and not lab frame. Concerningly, I just learned that momentum in cm frame is always zero. And the derivation for final velocities under elastic collisions is sooo much faster and less work in the cm frame than the lab frame. Supposedly collison problems are much easier in the cm frame so I hope that’s true. This topic, might genuinely be my weakest cause on past f=ma exams I struggled with it
Note: When I was studying on a cruise last year during Thanksgiving break, I remember trying to derive the equations for final velocities in elastic collision and I ended up with nearly two pages of very messy work—an abomination of energy and momentum equations, which got extremely messy with all the squares. The typical collision problems I have done in school and non-competitive resources usually give you the final velocity of at least one, and the starting of both. In some setups, however, only the initial velocities are given.
Note: After learning some cm frame tricks, the final velocities in elastic problems have become significantly easier.