n astronaut having mass 320 kg with equipment included is attempting an untethered space walk. The astronaut is initially at rest with respect to the nearby spacecraft, but discharges 30.0 g of nitrogen gas at 900.0 m/s from a portable propulsion unit. How fast is the astronaut moving after doing that? 0.36 m/s, 0.084 m/s , 27 m/s, or 84 m/s ?? :/

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n astronaut having mass 320 kg with equipment included is attempting an untethered space walk. The astronaut is initially at rest with respect to the nearby spacecraft, but discharges 30.0 g of nitrogen gas at 900.0 m/s from a portable propulsion unit. How fast is the astronaut moving after doing that? 0.36 m/s, 0.084 m/s , 27 m/s, or 84 m/s ?? :/

Physics
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here we have to apply the momentum conservation law
ok!
so we can write this: \[P = 0.03 \times 900 = ...\] is the momentum of the gas discharged

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Other answers:

oops..discharged gas
how much is P?
errr 27?
ok!
the momentum gained by our astronaut is: \[P' = 320 \times V\] where V is his velocity
so we can write: \[27 = 320 \times V\] what is V?
0.984375? so our solution is 0.084 m/s ?
\[V = \frac{{27}}{{320}} = {\text{0}}{\text{.084375}}\]
so V=0.084
so is that our final solution? :O
yes!
yay!! thank you!!
thank you!! :)

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