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 140 kg. During a space-walk, the unit, which has been filled with propellant gas, ejects some gas with a velocity of +33.2 m/s. As a result, the astronaut recoils with a velocity of -0.180 m/s. After the gas is ejected, the mass of the astronaut (now wearing a partially empty propulsion unit) is 180 kg. What percentage of the gas propellant in the completely filled propulsion unit was depleted?

Explanation / Answer

Let mp = the total mass of the propellant in a full propulsion unit. Assuming the gas the astronaut ejected was done so instantly, then the forces (F=m*a) on the ejected propellant and the astronaut are: F(astronaut) = 180 kg * (-0.180 m/s) = -32.4 N F(propellant) = (140 kg + mp - 180 kg) * (33.2 m/s) Because of Newton's 3rd law, the force on the gas is equal and opposite to the force on the astronaut: F(propellant) = -F(astronaut) (mp - 40 kg) * 33.2 m/s = 32.4 N Solving gives mp = 40.976 kg We also know that the amount of propellant left is 180 - 140 = 40 kg So, the percentage depleted (used) is 100 * (40.976 - 40) / 40.976 = 2.38%

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