Hard trajectory of equilateral triangle system I was doing this problem in physics class,

Time is easy to solve for, using the velocity of approach and dividing the initial separation by it.
Otherwise, I am interested in the trajectory of these particles. 
In order to solve for the trajectories, I tried to make use of the unit vectors along the sides but the resulting equations have moduli in them which I don't know how to integrate.
To try a different track, I wondered if it would be fruitful to try a complex number approach.
Is there a way to do this using vectors or complex numbers(Or otherwise)?
Thanks in Advance!


Please understand that a sufficient knowledge of polar coordinates is necessary to understand this solution and even then this is quite a rough calculation for one particle. Hope this helps.
