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.

Answer 1

Initial separation between two particles=Side of hexagon=a
Final separation=0
Therefore,
Relative displacement between two particles=a

Particle B has a component
v cos 600 along particle BC (a side)

Therefore, relative velocity with which B and C approaches each other=v- vcos60
=v/2
Since, v is constant, thus time taken by these two balls to meet each other is given by
=(Relative displacement) / Relative velocity
=a/(v/2)=2a/v
So, the time taken by the particles to meet each other=2a/v