by lennyp
 Emeritus Sci Advisor PF Gold P: 9,789 Taking the expression for kinetic energy, note we are ignoring gravitational potential energy here since we are considering the velocity of the balls just after and before collision; $$\underbrace{\frac{1}{2}mv^2}_{\text{First Ball}} = \underbrace{\frac{1}{2}mv'^2}_{\text{Second Ball}}+\underbrace{\frac{1}{2}mv'^2}_{\text{Third BallBall}}$$ Now, all you need to do is plug in the value for $v'$, which is the velocity of the second two balls, and check the equality.