# Will they ever meet?

**Classical Mechanics**Level 4

Consider three particles \(P,Q,R\) which are situated at the vertices of equilateral triangle \(ABC\) of side \(1\text{ m}\) .Each of the particles move with constant speed \(1 \text{ m/s}\). \(P\) always has its velocity along \(AB\), \(Q\) always has its velocity along \(BC\) , \(R\) always has its velocity along \(CA\). At what time in seconds will the particles meet each other?

If you think that they will never meet , prove it and enter the answer as 1.1.

If you think that they will meet at infinity , prove it and enter the answer as 2.2.