Quote:

a momentum magnatude of -1

You still don't know what magnitude means? Why don't you look things up instead of forcing yourself to remain confused?


Momentum is not force. If it was we'd call it force instead of momentum.

This is a 1-dimensional elastic collision! Nothing could be simpler. This is what teenage science students do every day. I think you just need to do some study.

Or get two coins and slide them against each other on a smooth table top.


Summary
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I a 1D elastic collision:

I say - total momentum before = total momentum after

You say - sum of magnitides of momentums before = sum of magnitudes of momentums after.