Problem #PRU-100682

Problem

A billiard ball lies on a table in the shape of an acute angle. How should you hit the ball so that it returns to its starting location after hitting each of the two banks once? Is it always possible to do so?
(When the ball hits the bank, it bounces. The way it bounces is determined by the shortest path rule – if it begins at some point $D$ and ends at some point $D^{\prime }$ after bouncing, the path it takes is the shortest possible path that includes the bounce.)