A cylindrical tube that is \(2.20 \mathrm{~m}\) long and has a radius of \(150 \mathrm{~mm}\) is filled with water. It is oriented with its long central axis vertical, and it is open to the air at the upper end. A hole \(80.0 \mathrm{~mm}\) in radius is drilled in the bottom, and the water is allowed to drain out. When the water level is half the height of the tube, \((a)\) what is the speed of the water exiting though the hole, \((b)\) at what rate (in meters cubed per second) is the water leaving the tube, and (c) how fast is the top of the water column falling?