Two billiard balls are rolling on a perfectly level, frictionless pool table. The first one is moving purely in the $+x$ direction at a speed of 1.5 m/s. The second is moving purely in the $+y$ direction at a speed of 2.3 m/s.
Both balls have the same mass. After a perfectly elastic collision, the first billiard ball is observed to have an $x$-component of its velocity as being 1.1 m/s, and its $y$-component of velocity is positive.
What is the magnitude of ball 1's final $y$ velocity?