Start with Newton's third law of motion, toss in the impulse-momentum theorem, and see what happens.
|+(p1 − p10) =||−(p2 − p20)|
|p1 + p2 =||p10 + p20|
Momentum is conserved. The total momentum of a closed system is constant.
1668: John Wallis suggests the law of conservation of momentum
The symbol p may be used for momentum because it is the mirror image of the letter q. Some people use p to represent the momentum of one object and q to represent the momentum of the other object in a recoil situation. A clever way to write Newton's third law of motion is like this…
+p = −q
action is equal and opposite reaction