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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?