CEMC Pascal, 1998

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

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?

(A) $9$ (B) $8$ (C) $7$ (D) $5$ (E) $4$

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