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}

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