A bomb with a mass of 4.0 kg explodes into three pieces (all the pieces travel parallel to the ground). The first piece with a mass of 1.0 kg travels at 5.0 m/s at an angle of 20° south of east. The second piece has a mass of 2.0 kg and travels 3.0 m/s at an angle 45° north of east. What is the velocity of the third piece?