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 +37 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 = %

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).(37) + (-(165)(0.39) = 0.

[Gas speed = 37 m/s

Astronaut speed = 0.39 m/s in opposite direction].

Mass of gas ejected = (165)(0.39) / 37

= 1.74 kg

Total mass of gas originally = 19 + 1.74 = 20.74 kg

Percentage of original amount depleted = (1.74 / 20.74) X 100%

= 8.389 %

8.389 % of original amount depleted.

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