The affect gravity has on a bullet

[JoshHolloway]

This is a simple question. Since projectile has -g as the only y velocity component, does that mean if I were to shoot a gun with my arm fully exended and parallel to the ground, then the bullet would hit the ground within one second of firing the gun(assumming there was nothing in its way)? Is that right? My reasoning is because if it is falling towards the Earth at 9.8 meters per second per second, and I am certainly not 9.8 meters tall, then there is no possible way that the bullet would be in the air for more that a fraction of one second (assuming the everything in the experiment followed the conditions I stated).

 

[JoshHolloway]

By the way, I think I should have written "the effect gravity has on a bullet".

 

[Integral]

You are correct. A bullet fired horizontally hits the ground at the same time one is dropped from the same height.

 

[JoshHolloway]

I would have never have believed that to be the case had I not learned about the gravitational constant in my physics class. Physics is hard, but it sure is cool!

 

[JoshHolloway]

I couldn't helf from noticing your avatar. Exuse my limited knowledge, but is it possible to take the definite integral from negative infinity to infinity?

 

[HallsofIvy]

The definite integral of what? It is possible for some functions (those that decrease very rapidly in both directions), not for others. Take the integral from A to B and then take the limits as A-> -infinity, B-> infinity. If those limits exist then $\int_{-\infty}^{\infty}$ exists.

 

[JoshHolloway]

wouldn't that just be infinity in many cases?

 

[rcgldr]

The bullets land at the same time only if the Earth is flat. With a spherical earth, the fired bullet lands just a bit after the dropped bullet.

 

[Integral]

For symetric functions it could as well be 0.

I think what most Physicist and Mathematians would ask where the differential is. The symbol I am using is really an incomplete expression. Perhaps one could call it a verb with no subject.

 

[masudr]

Well if the bullet is launched fast enough it might never hit the ground because the Earth keeps on curving away - that's (kind of) what we do with rockets.

 

[JoshHolloway]

I have heard of that masudr. Isn't that theoretically what is happening with satellites? They are continiously falling toward earth, but due to its curvature and their magnidude of velocity they stay about the same distance from earth. Is that correct?

 

[JoshHolloway]

If that is correct the bullet would have to go pretty damn fast to be able to do that. Is the gravitatioal force also less where the satellites are located when compared to objects much closo earth?

 

[HallsofIvy]

Yes to both, BUT. That is exactly what satellites do. Yes, the pull of gravity is less farther from the Earth (I drops off as 1/r²) but if you fire the bullet at high enough velocity it will get high enough. However, if we neglect air resistance, the bullet will not ever orbit the earth. If the initial speed is high enough its path will be a parabola/hyperbola and the bullet will just keep going. If not, its path will be an ellipse/circle with one focus at the Earth's center but the point on the Earth from which the bullet was fired will lie on that path so the bullet must hit the Earth eventually. Satellites that are put into orbit require and additional rocket "burn" to put them into orbit once they are high enough.

 

[batman1200]

wouldn't the aerodynamics of the bullet make it act a little like an airplane, and therefore stay in the air more?

 

[berkeman]

wouldn't the aerodynamics of the bullet make it act a little like an airplane, and therefore stay in the air more?

Welcome to the PF.

This thread has been dormant for 5 years, so I guess you found it with Google?

To answer your question, there is no "lift" associated with the bullet shape, only drag.

 

[batman1200]

Welcome to the PF.

This thread has been dormant for 5 years, so I guess you found it with Google?

To answer your question, there is no "lift" associated with the bullet shape, only drag.

yes, i did find this on Google,and i am new to pf, and don't get me wrong, i am no genius, but i was thinking that the arrow shape of the bullet would help it stay in the air longer. like the bottom of the boat pushes up on the bottom of a speed boat (the fast ones that at some points go air born). also, there are some new sniper bullets, i do not know how they do it, or exactly who made it, but they are pretty amazing. i think they where designed by barrett.

 

[K^2]

Yes, aerodynamic effects will make a difference. It's not going to work like an airplane, but the fired bullet does fall slightly slower. The reason for it is that drag is quadratic in velocity so bullets very high horizontal velocity contributes to the vertical drag. But vertical drag is still pretty small, so we are talking about a difference of a few ms.

MythBusters have performed an experiment. Their conclusion was that bullets hit at the same time. But if you look at the times they actually clock, they are slightly different, and the best estimate I was able to do, which admittedly was fairly crude, gave me the same order of magnitude for the time difference that they got. So the effect is there and it is measurable, but it's still very, very small. When aiming at a target, you can pretty much ignore the difference. (The aerodynamic effect on time-of-flight is significant, however, and you do have to take that one into account when aiming.)

 

[batman1200]

thank you for clarifying that for me

 

[sophiecentaur]

A bullet is symmetrical (and most of them also spin) so up and downward forces would balance out- hence no lift.

 

[batman1200]

is there anyone out there who would know a formula to calculate the speed of a bb of an air soft gun. for example, i want to know that if i shoot a bb weighing .12 gram out of a certain gun, and it went 466 feet per second, and a .2 gram bb shoot out of the same gun went 361 feet per second. what formula would i use if i wanted to know the velocity of a .2 gram bb shot out of another gun that shoots .12 gram bbs at a speed of 350 feet per second?

 

[JaredJames]

You would need to calculate the pressure produced in the barrel to expel the projectile, from there you could work out the speeds.

 

[sophiecentaur]

I believe the energy limit for a conventional airgun is 12ft lbs, so that should be enough to work out the speed from the KE if you know the mass. I really can't be naffed to do the sum in Imperial units, myself.

But, if you already have some performance figures, you could calculate the KE for the known bb mass and then do the inverse calculation for another mass.

 

[JaredJames]

I really can't be naffed to do the sum in Imperial units, myself.

Seconded

 

[sophiecentaur]

In 1972 (or whenever it was) the UK changed to decimal coin and I actually saw a woman converted to the idea at the checkout of a supermarket. She saw that the cost of ten items involved just putting a zero on the end of the cost of one. "That's fantastic" she said - and she was right.
Since then, no one with any sense (I could be sticking my neck out here, a bit, but hell.) has used non-decimals systems. Why are people using feet and inches and pounds and ounces still? The Romans didn't 'do' Arabic Numbers and look where that got them. Anyone ever hear of a Roman Scientist or Mathematician? Snap out of it all you dinosaurs. You know it makes sense.

 

[JaredJames]

All the nice easy mm values you get for nuts and bolts and people still insist on using fractions of inches.

The other day I was helping with a DIY project and was told a measurement of 2/8ths + 1/16th of an inch (or 1/4 + 16th of an inch as I noted).

Some wicked units out there though for non-decimal people to use.

I especially love when you get a mix, as above, 10mm pellet with 12ft.lbs. Lovely.

 

[sophiecentaur]

How many ergs would that be?
(Look it up young man - I did them at School)

 

[JaredJames]

I was ok with the definition up until it brought in dynes... then my head went into meltdown.

 

[sophiecentaur]

A really bloody silly unit - only relevant in a flea circus.