A space shuttle of inertia \(m\) is attached to a booster rocket that has an inertia nine times greater. This system is moving at a speed of \(800 \mathrm{~m} / \mathrm{s}\) in outer space, as seen by observers in a nearby space station. Then explosive bolts are detonated, separating the shuttle from the rocket and thrusting the shuttle forward at a speed of \(100 \mathrm{~m} / \mathrm{s}\) relative to the rocket. What are the velocities of the rocket and the shuttle right after the explosion?