Wow, I’m surprised nobody has mentioned the travel time for the information that the bullet has hit the ground! Since the soonest we can know that the bullet has hit is t=s/c (s is distance the bullet travels), the dropped bullet will always seem to land before the fired one. Sheesh. Amateurs.
wait, put down those torches! what’s that pitchfork for?
hahaha, come on, guys, I was only kidding! HEY!
::running away::
A common misconception about relativity, Joe_Cool. When you see an event happening is not when it seems to happen. If I see a supernova 1000 light-years away happen right now, I don’t say that it just happened right now: I say that, assuming it hasn’t moved since, it happened 1000 years ago, but I’m seeing it now. Where relativity comes in, is that different observers will disagree as to whether it’s moving, and thus on where it was when it went off.
Bringing this back to the matter at hand, a person trying to say which bullet landed first will take the light travel time into account. Although different observers will take it into account differently, as I posted above, the problem implies a particular frame of reference which we ought to use to solve the problem.
I typed this out in detail twice before, but my netscape crashed, and I don’t feel like typing it all up a again, so I hope this condensed version makes sence.
I know he said in a vacuum, but I’m more curious what happens in air.
Assume the bullet is fired at a speed greater than its terminal velocity. After the bullet leaves the barrel it has a lower than horizontal flight path,(aimed toward the ground.) Does the downward velocity component( accelerated by gravity) have to be greater than the terminal velocity before the effect of gravitation acceleration is effected, or does the fact that it has a total velocity greater than the terminal component, with a downward compontent, mean that it is going to not be accelerated quite as fast by gravity,(not quite getting 32 f/s). sort of a partial terminal velocity.
wolfman: Air resistance works to some degree at any velocity. How much resistance you have depends on the velocity: A simple model is that it’s directly proportional, so at double the speed, you get double the resistance: This is true faster or slower than terminal. What terminal velocity is, is the speed at which the force of air resistance is exactly equal to the force of gravity. So, to answer your question, no the speed does not have to be greater than terminal to have an effect.
Terminal velocity applies only to an object being accelerated by gravity and slowed by air resistance. It does *NOT* apply to any velocity component not on the vertical axis. Thus it has no effect on the range of the bullet. Furthermore, it acts equally on the fired (it's high horizontal velocity is irrelevant) and dropped bullets, therefore no effect overall.In air the moving bullet falls slower due to greater drag.
here’s the physics:
the speeding bullet begins to accelerate downward under gravity. The net velocity component is at a slight downward angle from the horizontal. the drag force is proprtional to the square of this velocity. the direction of the drag force is opposite the velocity. there is thus a small component of the drag force in the upward direction opposing gravity. this force component is larger that the equivalent upward drag force on the dropped bullet, due to the higher overall velocity.
(note drag scales quadratically with velocity. if it were linear then this argument would fail)
in vaccum the two bullets fall at the same rate. to see this put yourself in the center of mass frame moving at 1/2 the velocity of the fired bullet. From your point of view both bullets are travelling away from you at exactly the same speed in opposite directions. you cant tell which one was fires and which one was dropped.
this argument breaks down in air because in staionary air we can determine which bullet is ‘moving’ faster through the air, breaking the symmetry.
Ya know, I think that bigkahuna has a point… In actuality, air resistance is more complicated than pure linear or pure quadratic, and which is the best model depends on the speed, but there are certainly higher-order terms, in which case I think that bk’s argument is valid. Let me be the first to admit that I was wrong.
ok, i’m harking back to high school physics, but here goes.
bullets these days store their own gunpowder. makes it convenient, that does. it seems to me that the explosion isn’t absolutely instantaneous, and that for a short distance the bullet may be projected straight forward, without any drop. it would be like a little jet pack or something.
then i got thinking, i’m a putz. if the barrel is perfectly flat, then the bullet can’t fall until it leaves the barrel. so the 6 inched (2 feet, whatever, keep the bullet in the air a little bit longer (however long it takes to get the bullet out of the barrel).
if you dropped the bullet when hte shot bullet left the barrel (the “at the same time” seems open to debate) than scratvh that last point. the rocket thing, and friction in the barrel (even in a vacuum) still seem valid.
maybe.