Conservation of Linear Momentum of astronaut

[rmarkatos]

I am pretty sure i have this question correct but i want to make sure it is likely to show up on a test

An astronaut is motionless in outer space. Upon command the propulsion unit strapped to his back ejects some gas with a velocity of 32m/s and the astronaut recoils with a velocity of -30m/s. After the gas is ejected the mass of the astronaut is 160kg. What is the mass of the ejected gas?

well after looking at external and internal forces they should both equal zero.
So i found that Pf=Pi is that correct? But the initial conditions are zero because the astronaut was motionless in outer space. I am going to call m1 and vf1 the astronaut and m2 and vf2 the propulsion unit.

m1vf1+m2vf2=0

160kg(-30m/s) + m2(32m/s)=0
-4800kg m/s +m2(32m/s)=0
m2(32m/s)=4800kg m/s

solving for m2 i got 150kg. is that correct?

 

[radou]

Yes, appears correct.

 

[kyle8921]

Your understanding of the conservation of linear momentum seems to be correct. The equation you used, m1vf1+m2vf2=0, is the correct representation of the principle. By setting the initial momentum (Pi) to zero, you are taking into account that the astronaut was initially motionless. Your calculation of m2, the mass of the ejected gas, also seems to be correct. This type of question is commonly used in tests and quizzes to assess students' understanding of the conservation of linear momentum. Keep up the good work!