A hockey puck of mass 4m has been rigged to explode, as part of a practical joke. Initially the puck is at rest on a frictionless ice rink. Then it bursts into three pieces. One chunk, of mass m, slides across the ice at velocity vi^. Another chunk, of mass 2m, slides across the ice at velocity 2vj

Determine the velocity of the third chunk.

Express your answer in terms of the variable v⃗ and unit vectors i^, j^.