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The law of conservation of momentum, which is a direct consequence of Newton's second law.

F = ma

If you look at both balls as a system, there is no external force, hence

ma = 0

(technically, there may be gravity but we are only concerned with forces in the x and y directions)

acceleration is the derivative of velocity

a = dv/dt

m dv/dt = 0

now integrate

m*v = constant = momentum

Keep in mind that we are talking about a system, so the formal equation to consider is

m1*v1,0 + m2*v2,0 = m1*v1,f + m2*v2,f

this is true for both the x and y components of velocity.

To fully solve the final state, we need one more equation. Usually this is given by knowing the coefficient of restitution or, in the case of c=1, conserving energy.

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