n particles are placed at the vertices of a regular n-sided polygon of side a. They start simultaneously with equal speed v, each always heading towards the next particle. Their collision time is:
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n particles are placed at the vertices of a regular n-sided polygon of side a. They start simultaneously with equal speed v, each always heading towards the next particle. Their collision time is:

G1 Physics · Accepted Answer

For adjacent particles, the angle between their instantaneous velocity components along the joining side is 2π/n. The rate at which one side shrinks is the relative approach speed: vᵣ = v-v cos(2π/n) = v[1-cos(2π/n)]. Initial side length is a. Therefore collision time is t = a / {v[1-cos(2π/n)]}.