A 2.40 kg stationary package explodes into three parts that then slide across a frictionless floor. The package had been at the origin of a coordinate system. Part 1 has mass m1 = 0.490 kg and velocity(14.0i+14.0j)m/s . Part 2 has mass m2 = 0.780 kg and a speed of 17.0 m/s, and travels at an angle 79.1° (counterclockwise from the positive direction of the x axis). (a) What is the speed of part 3? (b) In what direction does it travel? State your direction as a positive (counterclockwise) angle from the +x axis.

This is simple application of the conservation of momentum. Since the initial momentum of the object is zero, the vector sum of mass times velocity for all three of the resuting pieces must add to zero.