Six particles situvated at the corners of a regular hexagon of side a move at a constant speed v. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particle will take to meet each other.

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Solution

A approaches B, B approaches C and so on.

Relative velocity between A and B,

${\to V}_{A B} = {\to V}_{A} - {\to V}_{B} = \to V c o s 60^{0}$

= $\to v - \frac{\to V}{2} = \frac{\to V}{2}$

Time, t = $\frac{d i s p l a c e m e n t}{V e l o c i t y}$

= $\frac{a}{\to V / 2} = \frac{2 a}{\to V}$

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Six particles situvated at the corners of a regular hexagon of side a move at a constant speed v. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particle will take to meet each other.

A approaches B, B approaches C and so on. Relative velocity between A and B, →VAB=→VA−→VB=→V cos 600 = →v−→V2=→V2 Time, t = displacementVelocity = a→V/2=2a→V

A approaches B, B approaches C and so on.

Relative velocity between A and B,

${\to V}_{A B} = {\to V}_{A} - {\to V}_{B} = \to V c o s 60^{0}$

= $\to v - \frac{\to V}{2} = \frac{\to V}{2}$

Time, t = $\frac{d i s p l a c e m e n t}{V e l o c i t y}$

= $\frac{a}{\to V / 2} = \frac{2 a}{\to V}$