Conservation of Kinetic Energy
In a perfectly elastic collision no kinetic energy is lost.

   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. 

Conservation of kinetic energy gives,

  

(1)

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

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