A canon shell moving along a straight line bursts into two parts. Just after the burst one part moves with momentum 20 N s making an angle 30° with the original line of motion. The minimum momentum of the other part of shell just after the burst is

As shown in the figure, the components of momentum of one shell along initial direction and perpendicular to initial direction are

$P_{1x}$ =$10\sqrt{3}$N s and $P_{1y}=10Ns$. 

For momentum of the system to be zero in y-direction, $P_{2y}$ must be 10 N s. The second part of the shell may or may not have momentum in x-direction $P_{2,min}$ = 10 N s.