1998 Pascal Problem 16

On a rectangular table 5 units long and 2 units wide, a ball is rolled from point P at an angle of 45^\circ to PQ and bounces off SR. The ball continues to bounce off the sides at 45^\circ until it reaches S. How many bounces of the ball are required?

\textbf{(A)}\ 9\quad \textbf{(B)}\ 8\quad \textbf{(C)}\ 7\quad \textbf{(D)}\ 5\quad \textbf{(E)}\ 4

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Full credit to this problem is given to the CEMC, you may view all Pascal contests here.