Final answer:
The second piece of the exploded missile has a momentum of 12.5 kg m/s to the right to conserve the total momentum of the system.
Step-by-step explanation:
When a missile explodes into two pieces and one piece has a momentum of 12.5 kg m/s to the left, by the law of conservation of momentum, the total momentum of the system must remain constant, assuming no external forces are acting on it. Therefore, the momentum of the second piece must be 12.5 kg m/s to the right (Option a). This is because the momentum of the system before the explosion was zero (since the missile was not moving), and after the explosion, the momenta of the two pieces must cancel each other out to maintain a total momentum of zero.