Duck, incoming rock!

Classical Mechanics Level 3

You tie a \(1~\mbox{kg}\) mass to the end of a \(1~\mbox{m}\) long string. The string has a breaking tension of \(200~\mbox{N}\) and you swing it in a vertical circle faster and faster. At the very bottom of one swing the string breaks and the mass flies off horizontally from a height of \(1~\mbox{m}\). How far has the mass gone horizontally in meters when it hits the ground?

Details and assumptions

The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).

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