# 1D Elastic Collision with restitution coefficient

I have an exercise about a 1D collision with a certain restitution coefficient, that is: $$e = \frac{|u_1-u_2|}{|v_1-v_2|}$$ One must calculate the velocities of the 2 colliding masses after the collision, with the mass and initial velocities given. They collide head-on, and thus the motion is all on the $$x$$-axis if you will. I found 2 solutions (obviously as you have to solve a quadratic equation), but they are both quite possible. One of the solutions has both masses moving in the same direction as they were before the collision but with a smaller magnitude and the other has them both traveling opposite the direction they originally came from. How do you determine which of the 2 solutions is more likely in such a scenario?

• Check your working as one of the solutions should be the initial conditions. Mar 29, 2021 at 22:49
• Well normally one of them would be if you just solve it without the restriction of the restitution coefficient, but here that isn't the case. I get 2 different solutions and neither of them is the inital condition. Mar 29, 2021 at 23:09
• Moving in the same direction . . . . but with smaller magnitude implies that momentum has not been conserved. Mar 30, 2021 at 6:19
• I mean i guess that the second option is just if the particles pass through one another. Mar 30, 2021 at 10:08