Puzzle #14 – Cue the Queue

Imagine an infinite row of regularly spaced billiard balls. The diameter of the balls is d and their centre-to-centre distance is D. The centres of the balls lie on a common axis.

You strike the first ball at a small angle \theta_0 to the axis. The balls collide elastically.

billiards

Question: Assuming the balls are signficantly further apart than they are wide, after approximately how many collisions between balls is the chain broken?

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