 Solution

In the initial centre-of-mass frame, equal fragments acquire opposite velocities $\pm w$ by conservation of momentum. The released energy isThe equal-mass fragmentation energy budget needs $w=500\mathrm{m}{\mathrm{s}}^{-1}$ merely to match the other ship, costing $1.25\mathrm{GJ}$. To close an existing gap requires a little more than this. Using the full reserve givesThe reserve is sufficient to overtake. The rear half moves at $1.368\mathrm{km}{\mathrm{s}}^{-1}$, preserving momentum. The kinetic-energy increase is the same in any inertial frame because total momentum is unchanged. Subsequent capture or braking would require additional interaction details; no target mass is needed for the interception test.