Two balls, A and B, impact each other as shown. If the coefficient of restitution, e, is 1.0 (perfectly elastic), what is the velocity magnitude of ball B after impact?

Velocity of Balls
Before and After Collision

Ball B only has a velocity in the y-direction, so first consider y-direction momentum. Conservation of momentum before and after impact gives

     m_Av_A1y + m_Bv_B1y = m_Av_A2y + m_Bv_B2y
     4 cos30 - 3 = -v_A2y + v_B2y
     0.4641 = -v_A2y + v_B2y

There are still unknowns, so the impact equation needs to be used,

     e = (v_B2y - v_A2y)/(v_A1y - v_B1y)
     1 = [v_B2y - (-v_A2y)] / [4 cos30 - (-3)]
     3.464 + 3 = v_B2y + v_A2y
     6.464 = v_B2y + v_A2y

Combining both equations
     0.4641 = -(6.464 - v_B2y) + v_B2y
     0.4641 + 6.464 = 2v_B2y
     v_B2y = 3.464 m/s

v_B2y = v_B2 = 3.464 m/s