A 0.490 kg hockey puck moving east with a speed of 5.20 ms has a head-on collision with a 0.830 kg puck initially at rest Assume a perfectly elastic collision?

Answer 1

I won't do all the algebra but here's the setup; Both momentum and kinetic energy are conserved in an elastic collision so you set the known momentum of puck 1, before the collision equal to the sum of the unknown momentum's of puck1 & puck2 after the collision. You then set the known kinetic energy of puck1 before collision to the sum of the kinetic energies of puck1 & puck2 after the collision. This gives you two equations in the unknown velocities after the collision. Solve for one velocity from the momentum equation, square it and substitute it in the KE equation. This will give you a quadratic equation in one unknown velocity. Solve for the two possible solutions. Try each solution back in the original momentum equation. One solution will give a non physical result so you discard it and use the one that gives you a physically possible solution. One possible nonphysical result is if puck2 remains at rest and puck1 continues East (positive velocity). I chose East as positive for convienence. So if an unknown velocity comes out negative it means its moving West.