A pile weighing 2000 lb is driven vertically into the ground by a pile-driver hammer weighing 6000 lb which falls freely from rest through a height of 16 ft to the head of the pile. The impact of the hammer on the pile is assumed to be inelastic; the hammer sticks to the pile. The resistance of the ground can be assumed uniform and equivalent to a force of 150,000 lb. Find how far the pile penetrates into the ground at each blow.