Linear momentum and relative velocity

1. The problem statement, all variables and given/known data

A space vehicle is traveling at 5300 km/h relative to the Earth when the exhausted rocket motor is disengaged and sent backward with a speed of 97 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?

2. Relevant equations

p=mv

3. The attempt at a solution

I found the initial linear momentum of the space vehicle (5)(5300) = 26500
Then found the relative speed of the command modular by setting the momentum of the exhausted rocket and the module equal. (26.9 m/s)(4m) = (v)(1m) solving v=107.6 m/s or 387.6 km/h. I don't understand how to express the velocity relative to the earth though.
 

LowlyPion

Homework Helper
3,055
4
1. The problem statement, all variables and given/known data

A space vehicle is traveling at 5300 km/h relative to the Earth when the exhausted rocket motor is disengaged and sent backward with a speed of 97 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?

2. Relevant equations

p=mv

3. The attempt at a solution

I found the initial linear momentum of the space vehicle (5)(5300) = 26500
Then found the relative speed of the command modular by setting the momentum of the exhausted rocket and the module equal. (26.9 m/s)(4m) = (v)(1m) solving v=107.6 m/s or 387.6 km/h. I don't understand how to express the velocity relative to the earth though.
Welcome to PF.

The center of mass of the system has a velocity of 5300 km/h.

Focus then on the momentum of the two separating objects.

What does the conservation of momentum tell you about the momentum of each of the parts with respect to the other? Since you know the relative masses then shouldn't you be able to figure the relative proportion of the two velocities - in opposite directions - that together make for a speed of separation of 97 km/h?
 
Ah, yes, thank-you so much!
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top