Can you help judge a physics bet?

[King_Stig]

Hello. A friend of mine stated the following;

If you stand on top of a moving plane (v=1000km/h) and shoot a bullet from a gun (muzzle velocity under normal conditions = 1000km/h) in the same direction that the plane is moving. He claims that the bullet will not leave the gun or if it does only barely. This is because of the resistance in the air.

I on the other hand claim this is complete rubbish, and the bullet will attain a much higher speed than 1000km/h in total.

Will you please be the judges. 40$ at stake here ;)

Thx.

-Stig

 

[Pengwuino]

Ah the ol relative velocity problem! What makes me curious is why he thinks if it did pick up extra speed, that it would be marginal. Bullets can certainly go far beyond supersonic.

That's besides the point, however. The problem with how a lot of people see this situation is that they don't realize the bullet in the chamber is moving 1000km/h even if its sitting in your hand! It's a matter of what frame of reference you look at. Since this question is assumed that someone on the ground is watching the plane travel by at 1000km/h, the ground is the rest frame. When the bullet fires, the force of the explosion will act on the bullet the same amount and for the same duration as if you were standing on the ground. From the person on the plane holding the gun's point of view, he will see the bullet fire off at 1000km/h, but more importantly, the person on the ground will see it travel off at 2000km/h. Now of course, there is going to be more air resistance if you're in a plane and you fire the gun, but, as some elementary calculations will do, you can approximate the resistance to be proportional to the velocity of the bullet, thus it will only face twice the air resistance. Worst case scenario in this approximation, the bullet slows down twice as quickly as if fired on the ground... which is not much.

Here's something to think about. Fighter jets have always had machine guns and canons mounted to them and even though they surely had more power behind them, they didn't just limp out of the barrels.

 

[King_Stig]

Thank you for a great (and qiuck) reply.

Victory is mine. muhahaha.

-S