Answer: and
Explanation:
An elastic collision is one in which both the total kinetic energy of the system and the linear momentum are conserved. That is, during the collision there is no sound, heat or permanent deformations in the bodies as a result of the impact.
Now, in the case of the satellites described here, we have:
(1) Conservation of momentum
(2) Conservation of kinetic energy
Where:
is the mass of the first satellite
is the mass of the second satellite
is the initial velocity of the first satellite
is the initial velocity of the second satellite (we are told it is at rest)
is the final relative velocity of the first satellite
is the final relative velocity of the second satellite
Now, as we know the second satellite is at rest before the collision, equations (1) and (2) change to:
(3)
(4)
Solving this system of equations we have the equations for and :
(5)
(6)
Substituting the known values on both equations:
(7)
(8) This is the final relative velocity of the first satellite
(9)
(10) his is the final relative velocity of the second satellite