Solution

A body of mass $M$ at rest explodes into $3$ pieces, two of which of mass $M/4$ each are thrown off in perpendicular directions with velocities of $3\,\mathrm{m\,s^{-1}}$ and $4\,\mathrm{m\,s^{-1}}$, respectively. Find the velocity of 3rd piece with which it will be flown away.