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Question

Six particles situated 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 particles will take to meet each other.


A

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B

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C

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D

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Solution

The correct option is B


The particles will meet at the point o the center of hexagon.At any instance the particles will form a

hexagon with the same center O.

Let's focus on motion of A

At any instance velocity of A is making an angle 60 from the line AO

The component of velocity of A along AO will be vcos60=v2

This component is the rate of decrease of the distance AO

AO = a

time taken for AO to become 0 t = av2=2av

Alternate solution:

Velocity of A along AB is v

Velocity of B along AB is -v cos 60

= v2

So the rate at which the distance AB decrease is vv2=v2

t=av2

=2av


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