explain why analysis of energy and momentum is the only way to solve collisions
Because during collision, internal impact force between two objects cause to impart impulse according to newton's law which is equal to change in momentum that's why momentum conservation in collision is used.
In collision, only kinetic energy interaction takes place and it is not necessary that kinetic energy always conserved except in elastic collision . That's why energy analysis is used in collision.
Coefficient of restitution is also used to analyze collision.
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