1. The problem statement, all variables and given/known data A grenade of mass 1.2 kg is at rest on a smooth frictionless surface when it suddenly explodes into three pieces. A 0.5 kg piece flies off horizontally to the north at 3.0 m/s, a 0.3 kg piece flies off horizontally to the southwest at 4.0 m/s. What is the speed and direction of the third piece? 2. Relevant equations P=mv P123=P1+P2+P3 Cosine Law 3. The attempt at a solution Well, I know the mass and velocity of the first two pieces. I know the mass of the third piece due to the remaining mass from the total and it comes up to 0.4 kg. I know the momentum of the first two pieces. I know I have to draw a diagram and find the momentum of the unknown side, which would be P1+P2. Then, I can solve for v3 by dividing m3 from P1+P2. The problem, however is the direction. Since the second piece flies southwest, I'm assuming the angle is 45 degrees. That leaves me with two unknown angles. I can find this by using the Sine Law, but I don't know which angle to use. This is where I need help, what is the direction of the third piece? Could someone please show me the diagram and which angle would be it for the third piece. Just as a side note, the velocity of the third piece comes up to a negative number, so does that mean that the direction will be switched? Thank you very much for the help. This is for my exam that's tomorrow.