Mark H. answered 01/03/20
Tutoring in Math and Science at all levels
First, keep in mind that momentum is a vector quantity, and is always conserved. Therefore, the momentum before and after the collision must be the same.
Before doing the details, let's establish a coordinate system: Using the typical x-y plot, let's define "right" as +x, and "left" as -x.
So--before the collision--Puck 1 has a velocity of -10, and Puck 2 has a velocity of +8. The total momentum is 8m - 10m = -2m
After the collision, the momentum is the same, but the combined mass is 2m. So the velocity (of both pucks) is -2m / 2m = -1
Based on the problem statement--with the pucks moving left and right--I would conclude there is no y component--in other words, all the action takes place along the x-axis. (No angles to calculate)