Four particles $P_1, P_2,P_3,P_4$ are moving in a plane. At $t=0$, they are at the four corners of a square $ABCD$ of edge length $l$. Each of the particles has a constant speed $v$. The velocity of $P_1$ is always directed to $P_2$, that of $P_2$ is always directed to $P_3$, that of $P_3$ is always directed to $P_4$, that of $P_4$ is always directed to $P_1$. At what time $t$ will all the four particles collide and where will they collide? Also how to calculate the angular acceleration of the line joining the particle and the final point of collision at any instant?
My attempt: First I assumed for any small time $dt$, any of the one particle moves a distance $v$ $dt$. Then for an adjacent particle the change in the angle (very small) $\Rightarrow$ $tan(d\theta)=\frac{vdt}{l}$ and it gives $\omega=\frac{v}{l}$. So all the particles are rotating with this angular frequency. But now how can we use this value of angular frequency? Firstly, I am finding it difficult to visualize the situation due to which I am not able to understand exactly what concept should we apply. Secondly, can we use linear equations of motion to approach this? Also can we view the motion with respect to a particle?
Found this on Wikipedia (Mice Problem/Pursuit Curve)
