Answer
$v_{2f} = 1.73~v_{1f}$
Work Step by Step
Let $M$ be the mass of each puck.
Before the collision, the y-component of momentum is zero. By conservation of momentum, the y-component of momentum must also be zero after the collision.
After the collision, the magnitude of the y-component of momentum of each puck must be equal. We can find the $v_{2f}$ in terms of $v_{1f}$:
$M~v_{2f}~sin~30.0^{\circ} = M~v_{1f}~sin~60.0^{\circ}$
$v_{2f} = \frac{(v_{1f})~(sin~60.0^{\circ})}{sin~30.0^{\circ}}$
$v_{2f} = 1.73~v_{1f}$
