A 5 kg sphere is connected to a fixed point O by an inexistensible string of length 5 m . The sphere is resting on a horizontal surface at a distnce 4 m from O. sphere is given a vertical velocity v0 and it moves freely till it reaches point p, when string becomes taut. Find the maximum allowable velocity v0 , if impulse of tension in string is not to exceed 6 N s.