A toy bomb that was initially at rest explodes into three pieces. Immediately after the explosion, a 320.-g piece moves with a speed of 2.00 m/s and in the direction 10.0° north of east while a 355-g piece moves with a speed of 1.50 m/s and in the direction 20.0° west of north. The third piece has a mass of 245 g. What is the speed and direction of the third piece immediately after the explosion? Assume there are no external forces.