Three particles A,B and C are situated at the vertices of an equilateral triangle of side l. Each of the particle starts moving with a constant velocity v such that A is always directed towards B,B towards C and C towards A. Find the time when they meet.

Options

A. `l/(sqrt(3)v)`
B. `(2l)/v`
C. `(2l)/(3v)`
D. None

Answer

C

Explanation

Relative velocity of apparoach
`v_(AB)=v_(A)-v_(B)cos 120`
Distance between A and B =l
`t=l/(v_(A)-v_(B)cos 120)=l/(v+v/2)=1/((3v)/2)=(2l)/(3v)`