I'm trying to explain to someone learning elementary physics (16 year old) that linear momentum and energy are conserved independently in a 2-body collision. I'm not a professional physicist and haven't tried to explain this stuff for years, and I can't think of any convincing elementary argument to show that this is the case. Does anyone know of an elementary approach to this? (i.e. one that does not contain the expressions "Lagrangian" and "Noether's Theorem".)
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