Conservation of Linear Momentum

[G-reg]

Homework Statement

A space vehicle is traveling at 6000 km/h relative to the Earth when the exhausted rocket motor is disengaged and sent backward with a speed of 86 km/h relative to the command module. The mass of the motor is four times the mass of the module. What is the speed of the command module relative to Earth just after the separation?

Homework Equations

Pi = Pf

m1vi +m2vi = m1vf + m2vf

The Attempt at a Solution

m1(6000) + 0 = m1(.64) + m2vf

which can be solved to..

m1(6000-.64) = m2vf

but I'm not sure how to get either m2 or vf
It seems like I would need vf to get m2

 

[anathema]

, but I also need m2 to get vf. Could you provide more information about the masses of the motor and module? Without that information, it is difficult to accurately solve for the final velocity of the command module. Additionally, it would be helpful to know if this is a conservation of momentum problem, in which case we would use the equation Pi = Pf, or if it is a conservation of energy problem, in which case we would use the equation KEi = KEf. Can you provide more context or information about the problem?

 

[tomcue]

, but I don't have enough information to solve for vf either. I would need the mass of the command module and the mass of the rocket motor in order to solve for vf. Without this information, it is not possible to accurately determine the speed of the command module relative to Earth just after the separation. Conservation of linear momentum states that the total momentum of a closed system remains constant, so the initial momentum of the system (before the separation) must equal the final momentum of the system (after the separation). However, without knowing the mass of both objects, it is not possible to accurately calculate their individual momentums and determine the final momentum of the system. Therefore, more information is needed in order to solve this problem.