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 Ee GO Tutorial

Explanation / Answer

Use conservation of momentum,

m = mass of propellant released

m * 37m/s = 165 kg * 0.39 m/s

m = 165 kg * 0.39 m/s / 37 m/s = 1.730 kg

Remaining propellant = 165 kg - 146 kg = 19 kg

% used = 100% * used / total = 100% * 1.73 kg / (19 + 1.73 kg) = 8.34%

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