It is a high pressure UEFA champions league final and the score is Juventus Barcelona 0 : 0 and the time left is 3 minutes of extra time. From somewhere Suarez provides a very good cross to Messi (our hero). As messi gets the cross he finds that Buffon (the Juventus goalkeeper) is in front of him.

Now Messi finds that with his hands full stretched Buffon can reach a height H which is also the height of the top goal bar and which is also the distance between Buffon and the goal base.

Messi flicks the ball (he is quite brilliant at it) at speed \(v\) at an angle of 45 degrees. The ball just clears Buffon and just gets inside the goal.

If \(v\) can be expressed as \(\sqrt{gh(x+\sqrt{y})}\), find \(x^{ 2 }+y^{2}\).

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