Answer: The total momentum before the docking maneuver is [tex]mV_{1}+MV_{2}[/tex] and after the docking maneuver is [tex](m+M) U[/tex]
Explanation:
Linear momentum [tex]p[/tex] (generally just called momentum) is defined as mass in motion and is given by the following equation:
[tex]p=m.v[/tex]
Where [tex]m[/tex] is the mass of the object and [tex]v[/tex] its velocity.
According to the conservation of momentum law:
"If two objects or bodies are in a closed system and both collide, the total momentum of these two objects before the collision [tex]p_{i}[/tex] will be the same as the total momentum of these same two objects after the collision [tex]p_{f}[/tex]".
[tex]p_{i}=p_{f}[/tex]
This means, that although the momentum of each object may change after the collision, the total momentum of the system does not change.
Now, the docking of a space vehicle with the space station is an inelastic collision, which means both objects remain together after the collision.
Hence, the initial momentum is:
[tex]p_{i}=mV_{1}+MV_{2}[/tex]
Where:
[tex]m[/tex] is the mass of the vehicle
[tex]V_{1}[/tex] is the velocity of th vehicle
[tex]M[/tex] is the mass of the space station
[tex]V_{2}[/tex] is the velocity of the space station
And the final momentum is:
[tex]p_{f}=(m+M)U[/tex]
Where:
[tex]U[/tex] is the velocity of the vehicle and space station docked
