A stationary bomb explodes into three pieces. One piece of 2 kg mass moves with a velocity of $8{\mathrm{ms}}^{-1}$ at right angles to the other piece of mass 1 kg moving with a velocity of $12{\mathrm{ms}}^{-1}.$ If the mass of the third piece is 0.5 kg, then its velocity is

Initial momentum is zero since the ball is stationary

Momentum of 2kg is $P_1 =2x8=16$ kgm/s

Momentum of 1 kg is $P_2 =1x12=12$ kgm/s

Both are at right angles so the resultant will be $P=\sqrt{{P_1}^2} +\sqrt{{P_2}^2}=\sqrt{256}+\sqrt{144}=20$ kgm/s

the third piece will have a momentum in the opposite direction to make the net momentum zero.
Therefore V = P/m = 20/0.5 = 40 m/s