The affect gravity has on a bullet

1. Oct 1, 2005

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).

2. Oct 1, 2005

JoshHolloway

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

3. Oct 1, 2005

Integral

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

4. Oct 1, 2005

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!

5. Oct 1, 2005

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?

6. Oct 1, 2005

HallsofIvy

Staff Emeritus
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.

7. Oct 1, 2005

JoshHolloway

wouldn't that just be infinity in many cases?

8. Oct 1, 2005

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.

9. Oct 1, 2005

Integral

Staff Emeritus
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.

10. Oct 1, 2005

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.

11. Oct 2, 2005

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?

12. Oct 2, 2005

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?

13. Oct 2, 2005

HallsofIvy

Staff Emeritus
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.

14. Jan 13, 2011

batman1200

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

15. Jan 13, 2011

Staff: Mentor

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.

16. Jan 13, 2011

batman1200

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.

17. Jan 13, 2011

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.)

18. Jan 14, 2011

batman1200

thank you for clarifying that for me

19. Jan 14, 2011

sophiecentaur

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

20. Jan 15, 2011

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?