An Australian bushman hunts kangaroos with the following weapon, a

heavy rock tied to one end of a light vine of length $2$ m$.$ He holds the other

end above his head, at a point $2$ m above ground level, and swings the rock in

a horizontal circle. The cunning kangaroo has observed that the vine always

breaks when the angle $($measured between the vine and the vertical$)$ reaches

$60$ o $.$ At what minimum distance from the hunter can the kangaroo stand with

no danger of a direct hit.