How many bullets does an astronaut need to fire to return to the space shuttle?

[lethal-octo]

Homework Statement

An astronaut is drifting away from the space shuttle at a velocity of 1.1m/s. He fires his gun's 30g bullets to return to his ship. The mass of the astronaut and his spacesuit is 123kg, his gun has a mass of 12kg and the bullets leave the gun at a velocity at 250 m/s.
What is the approximate minimum number of bullets that he will need to fire to begin drifting back to the ship?

Homework Equations

mv=mv?

3. The attempt at a solution
mv=mv*(number of bullets)
(135)(1.1)=(0.03)(250)*n
148.5=7.5n
n=19.8
Therefore the astronaut will need to fire 20 bullets to start drifting backwards. Is this right?

 

[Herman Trivilino]

mv=mv*(number of bullets)
148.5=7.5n

Are these velocities measured relative to the space shuttle?

 

[lethal-octo]

Are these velocities measured relative to the space shuttle?

I'm not really sure as this is a question from a practice exam, so I just plugged the variables in.

 

[haruspex]

Therefore the astronaut will need to fire 20 bullets to start drifting backwards. Is this right?

Yes. To be completely accurate you would need to take into account that the initial mass includes the bullets, and this reduces with each shot fired. But you are not told the total initial mass of bullets, and the effect would be tiny anyway.

 

[Dr. Courtney]

Another point that is missed in idealized textbook problems is that the recoil of the pistol is equal and opposite not only to the momentum of the bullet, but to the momentum of the bullet plus the momentum of the expanding gases that propelled the bullet (at least the component in the same direction). This complicates accurate computation of pistol recoil considerably and renders simple formulas based on bullet mass and velocity a significant underestimate.

The attached photo shows stills from a high speed video taken in our lab to try and better quantify the contribution of the gases. The frames in view do a pretty good job showing the forward motion of the gases. Later frames (not shown) allow quantifying the subsequent rearward motion of the pistol. Bullet velocity was measured with an optical chronograph.

 

[SteamKing]

Yes. To be completely accurate you would need to take into account that the initial mass includes the bullets, and this reduces with each shot fired. But you are not told the total initial mass of bullets, and the effect would be tiny anyway.

Presumably, the mass of the gun (12 kg) includes the mass of the bullets with which it is loaded.

 

[haruspex]

Presumably, the mass of the gun (12 kg) includes the mass of the bullets with which it is loaded.

Perhaps, but that is not at all clear.

 

[Herman Trivilino]

If the speed of the astronaut were a significant fraction of the muzzle speed, you'd have to take into account that the velocity of the bullets with respect to the gun is not the same as the velocity of the bullets with respect to the shuttle. In this case it's insignificant.