Understanding Head-On Collisions: Definition and Impact in Physics"

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i_island0
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will it be correct if i define head on collision something like this:
When, in a particular reference frame, the direction of velocities of two bodies lies along the common normal, the collision can be called head on even if their Center of masses doesn't lie along their common normal.
 
This is not a head on collision. The frame of reference doesn't matter. Resolve each v vector into 2 components, one (a) along the center line connection and the other (b) perpendicular. After the collision a becomes -a for each ball, while b is unchanged. The balls do NOT bounce back along their paths before collision, so it is not head on.