A bomb at rest at the origin of an xy -coordinate system explodes into three pie

Question

A bomb at rest at the origin of an xy-coordinate system explodes into three pieces. Just after the explosion, one piece, of mass 2.0 kg, moves with a velocity of 45 m/s in the negative x-direction, and a second piece, also of mass 2.0 kg, moves with a velocity of 13 m/s in the negative y-direction. The third piece has a mass of 6.0 kg. Just after the explosion, what is the magnitude of the velocity of the third piece?

Just after the explosion, in what direction is the third piece moving? (Give your answer as an angle measured counterclockwise from the positive x-axis.

Explanation / Answer

momentum conservation in vector form:

0=-2*45 i -2*13 j +6u i +6vj

So

6u=90 and 6v=26

So

u=15m/s {speed in positive x direction}

and

v=13/3=4.33m/s {speed in positive y direction}

So

mag. of vel.=sqrt(u^2+v^2)=15.6134m/s

and

direction=tan^-1(v/u)=16.11 degrees

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