A uniform rod AB, of length 2l and mass m, is free to rotate in the vertical plane about a smooth horizontal axis via A. The rod is free from rest if AB is horizontal. If the rod is vertical, a horizontal impulse is exerted at the middle point of the rod reverses the direction and halves the magnitude of angular velocity of the rod. Determine the magnitude of the applied impulse, and determine as well the impulse of the reaction on the rod at the point of support.