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. If the time taken by the particles to meet each other is $\frac{na}{v}$.Then $n$ is given by

Answer 1

for any two particles,

$V_{rel}=V-V\cos {60}^{\circ }$

$=V-V/2$

$=V/2$

distance $=a$ ($\because$ particle always points towards other)

$\therefore t=\frac{d}{V_{rel}}$

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