A bucket of mass `8 kg` is supported by a light rope wound around a solid wooden cylinder of mass `12 kg and radius 20 cm`, free to rotate about its axis. A man holding the free end of the rope with the bucket and the cylinder at rest initially, lets go the bucket freely downward in a well `50 m` deep. Neglecting friction, obtain the speed of bucket and angular speed of the cylinder just before the bucket enters water. Take `g = 10 m//s^(2)`.