And more to the point, how fast? Undergraduate physics 101 would say that it comes down with the same velocity it left the muzzle with. Then again, Physics 101 postulates mass-less ropes, frictionless pulleys, and spherical cows moving at twice the speed of light with flashlights taped to their spherical heads… So I’m guessing to calculate a trajectory to a second and more useful approximation, we’d need to put air resistance and the gyroscopic stabilisation back into the calculations.
Cecil has reported that a .30 caliber bullet shot into the air reportedly hit the ground at 300feet/ sec, but that seemed an entirely empirical result.
Any of the teeming millions know of a reference that someone reasonably well-versed in freshman physics and calculus, but not much beyond that, could follow, that would explain how to estimate drag and gyroscopic stabilisation for a projectile?
There’s no easy formula. I think you just need empirical data.
You can simplify the problem by ignoring the gun entirely. Start with the simplifying assumption that it will get the bullet high enough for the bullet to hit terminal velocity on the way down (it will). In that case, all you need to find out is the terminal velocity of the bullet. And that depends on its shape and weight.
All this below taken with the understanding that you mean a bullet fired straight up:
It would fall to the ground with much less speed than it left the muzzle of the gun. By the time it is falling, the only substantial force operating on it would be gravity, which would not make it fall as fast as it left the gun, undergraduate physics 101 notwithstanding.
If you want to follow a particular case, you need only calculate how high it will go from the initial shot, then how much gravity will accelerate it from that height (taking into account the friction from the air around it).
If you mean a relatively level flight, well… remember that it will be slowing down due to friction as soon as it moves. This could get pretty tough. Is there an artilleryman in the house?
I suppose if we got some specific data, we could try to get to work on it. I think empirical is the way to go here.
If I shot a bullet straight up in the air, would not the bullet go until it slows downs, either due to lack of forward enertia or atmospheric conditions (lack of air for the bullet to pass)?
Would not the bullet just fall to the surface at a different speed than its taking off point? Sounds reasonable to me.
If you dropped Michael Jackson’s baby and an elephant off a 100 story building, the baby and the pacaderm would hit the ground at the same time. For this to happen, what is the maximum speed that these two objects are going?
Would the speed change due to the density of the air (if the drop took place in Tibet or Miami) or does gravity reign supreme?
The elephant would hit the ground before the baby, for essentially the same reason that a tennis ball will hit the ground before a feather when dropped from the same height.
If you drop them from the same height above the ground in Tibet and Miami, they’ll be moving faster when they splat in Tibet than in Miami. Thinner air offers less resistance.
The bullet question depends on the speed at which air resistance acts with the same force on the bullet as gravity does, at which point it will maintain a constant velocity (well, slowing marginally as it nears the ground due to higher atmospheric pressure, if you want to get picky) until it hits the ground. What speed that is depends entirely on the mass and shape of the bullet, as previously mentioned. And whether it’s falling in a stable attitude or sort of tumbling, I guess.
We had an incident about five years ago during a New Year’s Eve festival, at midnight a man shot a pistol into the air and the bullet came down into the skull of a 12 year old girl who was watching the city fireworks. She did survive but is somewhat paralyzed.
Once you account for everything, the equations get so hairy you need either empirical results (IMHO, the only real way to get answers) or a computer. In the 1940s, the Navy chose the second route. Hence the earliest generation of computers were pressed into service computing artillery tables for Naval guns.
You can simplify the equations to your heart’s content, but at some point your neat sums no longer bear the slightest resemblence to reality.
Atmospheric drag is the perfect example of this: It’s easy to ignore something as innocuous as the air, but if you do it at the wrong times you convince yourself that if you dropped a feather and a ball bearing from the top of the Empire State Building, they’d both brain the people walking below equally well. Ain’t gonna happen on Earth, but it would work just fine on the Moon (and we have video evidence, thanks to the Apollo missions).
So a good answer would take into account not only gravity, but Earth’s atmosphere (say you’re at sea level to make things easy) and the mass and shape of the projectile (would it fall nose-first or base-first, or would it more likely tumble?).
But one thing that would make a big difference would be the tumble, or lack of, as the bullet falls. Derleth is backed up by gruven’s link: “A well-balanced bullet will fall base first. Depending on bullet design, some bullets may tumble on their way down and others may turn over and come down point first.” Other than that, though, I would think that you could make a pretty fair estimate of bullet terminal velocity, which would be a pretty fair estimation of actual ground-impact speed. Depends on how accurate you want to be, of course.
Further belaboring the point made by Gruven’s link and others
There is a persistent urban legend about pennies dropped of the Empire State Building. There is little danger of a penny dropped from the top actually killing someone, it would probably hurt a bit but that’s about it. The velocity and thus the kinetic energy would be considerably less than a hailstone of the same mass.
This is due to the hailstone being a sphere while the penny is a disk. As the penny falls it tumbles and thus presents a varying profile to the oncoming air. Without an accurate model of this tumbling motion it is impossible to accurately predict velocity or trajectory, although both can be approximated statistically. The same holds true for the bullet. As it looses velocity, both linier and radial it begins to tumble so during the return flight it becomes more difficult to predict velocity. It stands to reason, however, that it will be well below the initial muzzle velocity (typically in the range of 2500 to 4000 feet per second for a rifle).
All of that is well and good, but what would happen if you shot a bullet into a hole that went clear through the Earth’s core and opened on the other side of the planet?
More importantly, what would happen if 1,000,000,000 Chinese men jumped off chairs at the same time, yelled at the top of their lungs, and fired bullets into the air? Would the Earth be forced out of its orbit? Could I hear the yelling here in VA?
I have a huge field in my backyard. 50+ acres. When it’s plowed in the fall my son and I once took my replica muzzle loader out there with a lead slug. Shot it straight up. We were ready to leave because we didn’t hear it or see it come down when all of a sudden maybe 50 yards away we heard a THUD. and saw a puff of dust… Both us went " JEEZUS!!!"
Thanks for that link, gruven. Looks like the one Cecil used in the link in the OP… I did try googling for info, but mostly came up with game developers assuring us that the projectiles in their games did follow realistic models, without saying what those models are…
No, the only substantial force operating on the bullet is NOT only gravity. If gravity were the ONLY force, the bullet would indeed hit the gun with the same speed as when it was fired.
The whole point of the question is that there is a very significant other force, that of air resistance. Incidentally, the force of air resistance is dependent on the speed of the bullet, and the cross-section is presents to its direction of travel.
I bow to your statement with the excuse that I did not consider air resistance to be great in comparison to the gravitational pull exerted upon it or to the initial force. I will try to be clearer in the future.
When the bullet stops ascending and begins descending, the effect of friction is smal, and only becomes greater as the bullet moves faster.