From the law of the conservation of energy; the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision must be 1.
The term momentum is the product of mass and velocity. The principle of conservation of linear momentum states that total momentum before collision must be the same as the total momentum after collision thus the ratio of the total momentum after the collision to the total momentum before the collision must be 1.
Also, from the law of the conservation of energy; the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision must be 1.
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