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 of the astronaut (now wearing a partially empty propulsion unit) is 165 kg. What percentage of the gas was ejected from the completely filled propulsion unit?

Answer 1

Answer:

10.96%

Explanation:

Mass of astronaut and empty tank

146 kg

Mass of astronaut and partially empty tank

162 kg

Mass of gas in the tank

162-146 = 16 kg

Momentum after gas release

$m_1v_1+m_2v_2=0\\\Rightarrow m_1=-\frac{m_2v_2}{v_1}\\\Rightarrow m_1=-\frac{-162\times 0.39}{32}\\\Rightarrow m_1=1.97\ kg$

Total mass of gas = 1.97+16 = 17.97 kg

Percentage depleted

$\frac{1.97}{17.97}\times 100=10.96\%$

The percentage of gas ejected is 10.96%