Answer:
the speed of the command module relative to Earth just after the separation = 4943.2 Km/hr
Explanation:
Given:
speed of space vehicle =5000 km/hr
rocket motor speed = 71 km/hr relative to the command module
mass of module = m
mass of motor = 4m
By conservation of linear momentum
Pi = Pf
Pi= initial momentum
Pf= final momentum
Since, the motion is only in single direction
Where M is the mass of the space vehicle which equals the sum of motor's mass and the command's mass, Vi its initial velocity, V_mE is velocity of motor relative to Earth, and V_cE is its velocity of the command relative to Earth.
The velocity of motor relative to Earth equals the velocity of motor relative to command plus the velocity of command relative to Earth.
V_mE = V_mc+V_cE
Where V_mc is the velocity of motor relative to command this yields
substituting the values we get
= 4943.2 Km/hr
the speed of the command module relative to Earth just after the separation = 4943.2 Km/hr