Conservation of momentum astronaut problem

AI Thread Summary
An astronaut with a propulsion unit ejects gas at +30.9 m/s, resulting in a recoil velocity of -0.265 m/s. The astronaut's initial mass is 143 kg, and after gas ejection, it increases to 167 kg. Using the conservation of momentum, the equation needs correction to distinguish between the remaining gas and the expelled gas. The correct approach involves identifying the mass of gas left in the unit to determine the percentage of gas depleted. This problem illustrates the application of momentum conservation in a closed system.
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Homework Statement


An astronaut in his space suit and with a propulsion unit (empty of its gas propellant) strapped to his back has a mass of 143 kg. During a space-walk, the unit, which has been filled with propellant gas, ejects some gas with a velocity of +30.9 m/s. As a result, the astronaut recoils with a velocity of -0.265 m/s. After the gas is ejected, the mass of the astronaut (now wearing a partially empty propulsion unit) is 167 kg. What percentage of the gas propellant in the completely filled propulsion unit was depleted?



Homework Equations



p=mv



The Attempt at a Solution


-.265(astronaut + gas) = 30.9 (gas)
-.265(143 + x) = 30.9x
-37.846 -.265x = 30.9x
31.165x = -37.846
x = 1.214 kg


i don't really know where to go from here... can someone please help?
 
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You need to distinguish between the portion of gas left in the propulsion unit and the portion of gas expelled. You should be able to immediately figure out the portion in the container from the data given. Use the conservation of momentum equation to find the portion expelled.
nick727kcin said:

The Attempt at a Solution


-.265(astronaut + gas) = 30.9 (gas)
Correct this equation. The "gas" on the left is the portion left in the unit, which should not be an unknown. And get rid of that minus sign on the left.
 
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