Chapter 9, Problem 47P

A vessel 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 (−30 m/s) $\hat{i}$ and a second piece, also of mass m, moves with velocity (−30 m/s) $\hat{j}$. The third piece has mass 3m. Just after the explosion, what are the (a) magnitude and (b) direction of the velocity of the third piece?