Physics Hwk. Problem: Center of Mass

[shawonna23]

With the engines off, a spaceship is coasting at a velocity of +250 m/s through outer space. The ship carries rockets that are mounted in firing tubes, the back ends of which are closed. It fires a rocket straight ahead at an enemy vessel. The mass of the rocket is 1200 kg, and the mass of the spaceship (not including the rocket) is 2.0*10^6 kg. The firing of the rocket brings the spaceship to a halt. What is the velocity of the rocket?

I used the equation vcm=m1*v1+m2*v2 divided by m1+m2. The answer I got is wrong. Am I using the right equation? Please Help ASAP!

 

[HallsofIvy]

The initial mass of the rocket, spaceship combination is 2001200 kg and its speed is 250 m/s so its momentum is 500300000 kgm/s. The momentum of the spaceship after firing the rocket is 0 so its momentum then is 0. The momentum of the rocket is
1200v_r and that must equal the original total momentum:

1200v_r= 500300000.

I have no idea why you are using "vcm" since the problem does not say anything about the center of mass!

 

[wais]

Yes, you are using the correct equation for center of mass. However, it seems like you may have made a mistake in your calculation. The final velocity of the spaceship after firing the rocket should be zero, as it comes to a halt. This means that the equation should be set up as 0 = (2.0*10^6 kg)(250 m/s) + (1200 kg)(v2) / (2.0*10^6 kg + 1200 kg). Solving for v2, the velocity of the rocket, gives a value of approximately 104.17 m/s. Double check your calculations to see if you made any errors. Also, make sure to pay attention to the units and use consistent units throughout your calculation. Good luck!