Avessel at rest at the origin of an xy coordinate system explodes into three pieces. just after the explosion, one piece, of mass m, moves with velocity (-31 m/s) i and a second piece, also of mass m, moves with velocity (-31 m/s) j. the third piece has mass 3m. just after the explosion, what are the (a) magnitude and (b) direction (as an angle relative to the +x axis) of the velocity of the third piece?

Explanation:

The momentum of the first piece = m v =- m x 31 i kg m/s in - x direction  direction

The momentum of the second piece = -m x 31 j kg m /s in Y - direction

Total momentum = - 31 m( i + j )

To conserve momentum , the third piece must have momentum equal to this

and opposite to it

So momentum of the third piece  = 3m x V = 31 m ( i +j )

V = 31/3 ( i + j ) =

Magnitude of velocity V = √2 x 31/ 3  = 14.6 m / s

Its direction will be towards the vector i + j  ie 45° from x - axis in positive direction

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your answer is c! hope this : )