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 +32 m/s. As a result, the astronaut recoils with a velocity of -0.39 m/s. After the gas is ejected, the mass astronaut (now wearing a partially empty propulsion unit) is 165 kg. What percentage of the gas was ejected from the completely filled propulsion unit? (Pay attention to whether the masses include the gas propellant in the tank or not. Both masses include the propulsion unit, but may or may not include the propellant.)

Explanation / Answer

Let M be the inital mass of the Propellant and m be the expelled mass.

from conservation of momentum

Pi = Pf

0 = m x 32 m/s + 165 x -0.39

m = 2 kg

Final mass of the system is atronauts mass plus the remaining mass of the propellent

165 = 146 + M - m

M = 165 - 146 + 2 = 21 kg

%age off mass expelled is:

% = (2/21) x 100 = 9.52 %

Hence, % = 9.52 %

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