Conservation of Momentum
Momentum is the product of an object's mass and velocity. It is a vector. In any collision the momentum of the particles measured in any direction before the collision is equal to their momentum in that direction afterwards.

Conservation of linear momentum in the direction of the incident ball (i.e. horizontally), gives

   m1 = mass of incident (blue) ball.

   m2 = mass of target (red) ball.

   u1 = initial velocity of incident ball.

   v1 = final velocity of incident ball.

   v2 = final velocity of target ball. 

  

(1)

Remember that the target ball is stationary at first and so has zero initial velocity.

Conservation of linear momentum at right angles to the direction of the incident ball (i.e. vertically), gives

  

(2)

The initial vertical momentum is zero because the ball is moving horizontally.

  
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