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An object at rest explodes into three pieces of equal mass.One moves east at 20.0 m/s,a second moves southeast at 30.0 m/s. What is the velocity of the third piece?

The vector sum of the momenta of the three pieces must be zero, since it was zero to begin with. The two pieces for which the velocities are given have a net southward momentum of
m cos 45 * 30 = 21.21 m
where m is the mass of one piece. They have a net eastward momentum of
20 m + 30 m cos 45 = 41.21 m
The third piece must have a momentm which cancels these two components. From that you can get the direction and the speed.

The unknown m's will cancel out if you do it correctly

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  1. Why use cos 45?

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