What percentage of the gas propellant in the completely filled propuls

[thatgirlyouknow]

Homework Statement

An astronaut in his space suit and with a propulsion unit (empty of its gas propellant) strapped to his back has a mass of 143 kg. During a space-walk, the unit, which has been filled with propellant gas, ejects some gas with a velocity of +30.9 m/s. As a result, the astronaut recoils with a velocity of -0.265 m/s. After the gas is ejected, the mass of the astronaut (now wearing a partially empty propulsion unit) is 167 kg. What percentage of the gas propellant in the completely filled propulsion unit was depleted?

Homework Equations

Pfinal = Pinitial
P = mv

The Attempt at a Solution

-.265(astronaut + gas) = 30.9 (gas)
-.265(143 + x) = 30.9x
-37.846 -.265x = 30.9x
31.165x = -37.846
x = 1.214 kg

This can't be right, because the total after expulsion is 167 kg, meaning there is at least 24 kg of gas in the tank. Any ideas?

 

[Dick]

Look at -.265(143+x)=30.9x. The x on the left side represents the gas remaining in the tank. The x on the right side represents the gas ejected from the tank. You are using x to represent two different things. Can you straighten this up? Hint: I would replace 143+x with 167.

 

[G01]

Your equations for the mass of the astronaut is not correct.

The mass of the astronaut during this situation is effectively 167kg.

Let the mass of the gas be x. The total mass of the astronaut with full tank would be 167+x.

Can you take it from here?

EDIT: Dick you beat me by 3 minutes! I wasn't even close!

 

[Dick]

3 minutes is close! Not all of that represents thinking time.

 

[thatgirlyouknow]

Thank you both!