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 +40. 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?

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) * (40) + (-(165)(0.39) = 0.

[Gas speed = 40 m/s
Astronaut speed = 0.39 m/s in opposite direction].
Mass of gas ejected = (165)(0.39) / 40
= 1.6087 kg
Total mass of gas originally = 19 + 1.6087 = 20.6087 kg
Percentage of original amount depleted = (1.6087/ 20.6087) X 100%
= 7.806

Around 7.8% of original amount depleted.

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