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# Conservation of momentum in 2D

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An object at rest explodes into three pieces of equal mass. One moves east at 20 m/s; a second moves 45 degrees south of east at 30 m/s. What is the velocity of the third piece?

OK, I know that the initial linear momentum of zero must be conserved, so I can start summing my momentum in the x and y directions. I'm just confused about what sign (plus or minus) to put on the unknown piece. I don't know what quadrant it is in. Anyway, I divided the y-component by the x-component and got theta = 86.73 degrees and v final of the third piece is 21 m/s. Is this right?

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