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Let's say there was gun and a bullet with a mass of 1kg at rest. The bullet and guns speeds were 2 m/s in opposite directions after firing if I right the equations.

Kinetic energy

0.5m_{1}v_{1}^{2}+ 0.5m_{2}v_{1}^{2}= 0.5m_{1}v_{2}^{2}+ 0.5m_{2}v_{2}^{2}

Why doesn't this equation work when objects are at rest. Mathematically I can understand but why physcially. Can anyone explain what is happening to kinetic energy in this scenario. Why does conservation of momentum equation hold in in inelastic collisions but not this one. I understand some energy is lost but why is it not affecting momentum.

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# Conservation of momentum and energy question

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