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 particle will take to meet each other.
Solution:
Relative velocity $=v-v \cos \theta$
$V-\frac{v}{2}$
$=\frac{v}{2}$
$\mathrm{S}_{\mathrm{rel}}=\mathrm{a}$
Speed= $\frac{\text { distance }}{\text { time }}$
$\frac{v}{2}=\frac{a}{t}$
$t=\frac{2 a}{v}$