# Looks like an old problem(it is not)

**Classical Mechanics**Level 4

We have three particles each of mass \(m\) namely \(A,B,C\) placed at the vertices of an equilateral triangle of side length \(l\)

At \(t=0\), \(A\) starts moving towards \(B\), \(B\) starts moving towards \(C\), \(C\) begins moving towards \(A\), each with a velocity \(v\).

Find the distance(not displacement) travelled by \(A\) from \(t=0\) till the time when all the three particles collide with each other.

**Details and Assumptions**

1)The velocity of A is always directed towards \(B\) and is \(v\),and similarly for the other two particles.

2)\(l=7.5 metre\)

3)Ignore gravity and anything else.