Particles in triangular motion

Classical Mechanics Level pending

Any three particles \(A\), \(B\) and \(C\) are situated at the vertices of a triangular shaped wooden board \(ABC\) of identical side length \(l\) at time \(t = 0\) (in seconds).

If each of the particles moves with constant speed \(v\) (in \(\text{ m/s}\)) and the velocity of particle \(A\),\(B\) and \(C\) is always along \(AB\), \(BC\) and \(CA\) respectively.

Then at what time(in seconds) will these particles meet each other ?

Detail and Assumptions:

  • \(v = 2\text{ m/s}\).

  • \(l = 6\text{ m} \).

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