A cart is moving along +x direction with a velocityof `4 m//s`. A person on the cart throws a stone with a velocity of `6 m//s` relative to himself. In the frame of reference of the cart the stone is thrown in y-z plane making an angle of `30^@` with vertical z-axis. At the highest point of its trajectory, the stone hits an object of equal mass hung vertically from the branch of a tree by means of a string of length L. A completely inelastic collision occurs, in which the stone gets embedded in the object. Determine :
(i) The speed of the combined mass immediately after the collision with respect to an observer on the ground,
(ii) The length L of the string such that the tension in the string becomes zero when the string becomes horizontal during the subsequent motion of the combined mass.