A mysterious explosion in an unmanned \(6000-\mathrm{kg}\) spaceship coasting at \(5000 \mathrm{~m} / \mathrm{s}\) breaks the ship into two unequal parts, one twice as massive as the other. The smaller piece recoils in the direction opposite to the original path at \(3000 \mathrm{~m} / \mathrm{s}\).

(a) What is the velocity of the larger piece after the explosion?

(b) Discuss the energy changes resulting from the explosion.