Chase the particle

Click the link to see the graph

In the above graph, purple particle moves along $y$ -axis and green particle move such that its direction of motion is always towards purple particle. Both move with equal speed $u$ metres per second. If the initial separation between them is 30 metres. Find the separation between them when the velocity of the particle makes and angle of $\pi/6$ with $x$ -axis.

Note : In the above graph it may look like speed is not constant because in graph I have made rate of change of $p$ [ $\pi/6$ in this question] constant}