# Azhagu The Super Cop

Azhagu the super cop was chasing a super thief which had special powers because of which the thief can fly but at a constant height $$h$$ from the ground. After too too much of runing the thief gets tired and stops, seeing this Azhagu fires a bullet with some angle from ground having max. height $$3h$$.The bullet should have hit the thief.

But as soon as the bullet left the gun the thief starts to run once again with a constant velocity $$v \ ms^{-1}$$, but still Super Cop Azhagu's bullet hit's the thief .

Then the ratio of $$v$$ and horizontal velocity of bullet is of the form $$\dfrac {2k}{1+k}$$.

Find the value of $$3k^{2}$$.

Note:

• Assume all the conditions to be ideal
• Azhagu is on ground and the thief is flying at every instant of time
• Bullet missed the target once.
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