So can we apply conservation of momentum? Well in the horizontal direction we're ignoring air resistance so the net force on the pieces is zero. Now there were certainly some quite large forces acting on the the spaceship, otherwise it wouldn't have exploded. Don't these screw things up? No. Because those forces are between atoms that are part of our system. The different atoms are pushing and pulling each other, in a hideously complicated way, but they're all internal to the system. The net force acting on the system in the horizontal direction is still zero. So we can can apply conservation of momentum.
The initial momentum in the horizontal direction is zero. So the final momemtum should also be zero:
Solving for 
, we have
