Elastic Collisions (Oblique Impact)

FeDeX_LaTeX
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http://desmond.imageshack.us/Himg843/scaled.php?server=843&filename=23518417.jpg&res=medium

The crucial thing I'm not understanding here is how they know that after the collision (shown at the bottom of the picture), the horizontal velocities of each particle are reversed. Surely we don't know that, though? However, the direction after is important because I'm getting a different answer if I just try to get v or w by itself. When I draw my diagram for what happens post-impact, I'm not giving v and w a direction, I'm just labelling them as horizontal components. However, to solve this question I think you need to know which direction they're in.

Any help?

EDIT: Sorry about image quality. Co-eff of restitution is 3/4.
 
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Eh, never mind, sorry. I was being an idiot, of course it shouldn't matter. I was doing Newton's Law of Restitution the wrong way round...
 
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