An astronaut in his space suit and with a propulsion unit (empty of its gas prop

Question

An astronaut in his space suit and with a propulsion unit (empty of its gas propellant) strapped to his back has a mass of 146 kg. The astronaut begins a space walk at rest, with a completely filled propulsion unit. During the space walk, the unit ejects some gas with a velocity of +39 m/s. As a result, the astronaut recoils with a velocity of -0.39 m/s. After the gas is ejected, the mass of the astronaut (now wearing a partially empty propulsion unit) is 165 kg. What percentage of the gas propellant was ejected from the completely filled propulsion unit?

Percent depleted = %
Note: I've tried 91.86

Explanation / Answer

Mass of astronaut + partially empty unit = 165 kg Mass of astronaut (+ empty unit) = 146 kg Mass of gas remaining in unit = 165 - 146 = 19 kg. Momentum before walk = 0 Momentum after gas released = (mass/gas ejected).(35) + (-(165)(0.39) = 0. [Gas speed = 35 m/s Astronaut speed = 0.33 m/s in opposite direction]. Mass of gas ejected = (165)(0.39) / 35 = 1.83 kg Total mass of gas originally = 19 + 1.83 = 20.83 kg Percentage of original amount depleted = (1.83 / 20.83) X 100% = 8.82 Around 9% of original amount depleted.

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