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An object, hanging at rest, explodes, breaking into three pieces. Two pieces, one with twice the...

An object, hanging at rest, explodes, breaking into three pieces. Two pieces, one with twice the mass of the other, fly off perpendicular to one another with the same speed of 31.4 m/sec. The third piece has three times the mass of the lightest piece. Find the magnitude and direction of its velocity immediately after the explosion. (I defined this problem with the mass m going in the +x direction, the mass 2m going in the +y direction, and the mass 3m moving with some speed at an angle θ relative to the horizontal.)

Can you please show work on how you did this?

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