Fig. 1. (Color online) 2D elastic scattering of two identical hard spheres. (a) The cue ball dashes into the target ball at rest along the x-direction with a velocity v→ and an impact parameter b, the shortest distance between the centers of the balls. (b) The geometry at the moment of contact. The target ball acquires an impulse along the direction parallel to the line that connects the two centers of the balls, with the final velocity u2→. (c) The three velocity vectors u1→, u2→ and v→ constitutes a right triangle as shown by Eqs. (6) and (7).
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