Final answer:
To determine the velocities of a satellite and its launcher after separation, conservation of momentum and conservation of kinetic energy principles must be applied, setting up equations for both and solving them simultaneously.
Step-by-step explanation:
The question involves the application of the conservation of momentum and kinetic energy principles in physics to find the subsequent velocities of a satellite and launcher after separation.
According to the conservation of momentum, the total momentum before and after the event must be equal, as there are no external forces acting on the system.
Also, the provided kinetic energy is the sum of kinetic energies of both parts after separation. We can set up two equations: one for the conservation of momentum (m1v1 + m2v2 = 0, where m1 and m2 are the masses, and v1 and v2 are the velocities of the satellite and launcher, respectively) and one for the conservation of kinetic energy (½ m1v1² + ½ m2v2² = 5000 J).
Solving these two equations simultaneously will give us the velocities of both parts relative to the reference frame in which they were at rest before separation.