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If a person on a train moving at speed 100 km per hour is moving in opossite direction with speed of 10 km per hour, then person's speed is 90 km per hour. Adding or substracting velocity vectors makes perfect sense. But adding or substracting momentums doesn't, if it means adding or substracting two momentums that each belong to two DIFFERENT objects in an isolated system.

If in isolated system two balls are approaching each other from opposite directions ( friction is negligible ), one on the left with momentum of 160 and the one on the right with momentum 100, then since momentum is vector quantity the resultant momentum will be 60 and its direction will be to the left.

I know the two balls together represent a system, but at the end of the day they are still two distinctive balls each with its own momentum, so to me substracting the two momentums belonging to DIFFERENT objects is like ... I don't know ... apples and oranges.

I know that when they collide their individual momentums will change but total momentum will stay the same!

So is perhaps the main reason why we add or substract momentums of different objects ( like in the above example ) because system has net momentum of 60 even in a case where objects at collision experience impulse that equals the smaller of the two momentums ( that would be momentum of the ball going left -> M=100), the remaining momentum will still be 60?

thank you

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# Momentums as vectors

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