I Shot a Rifle into the Air…

Three questions about gravity and velocity answered.

Question  #1

If the rifle is fired straight up will the bullet pierce the head of the one who fired it when it comes back down ?

The answer is derived from physics, and is all about gravity’s effect on objects. There is a certain principle in science called a constant. This is a factor that has been determined to remain unchanged with certain caveats. Since conditions on the Earth vary, most constants are said to apply only within a vacuum. Meaning that, with the absence of air resistance gravity will act the same on any body. Therefore, the answer to the above question is obvious. If you stood next to someone and fired directly at them, obviously, the bullet would penetrate. The same is true if a projectile is shot straight up into the air. Acceleration has been measured at a constant 32 ft/sec2. The constant is the same whether the bullet is going up or down. Therefore, when the bullet is ascending it would slow at the same rate at which it speeds up on its descent. If you measured the speed of the bullet at any height along its trajectory both ascending and descending, that  speed would be identical. So, the bullet would penetrate because it would have attained the same speed when it reaches the person as it had when it left the rifle.

Question #2

If a rifle is held exactly perpendicular (i.e., horizontally from the ground) and fired while at the same time a bullet is dropped from the same height, which bullet will strike the ground first?

The question is somewhat convoluted. I am saying that if a person fires a rifle from a height of 6 feet, and a bullet is dropped at exactly that same time from an identical six feet, which of the two bullets (fired from a gun or dropped from the hand) will reach the ground first? Given the properties of gravity discussed in the first question the answer is obvious. They would both hit the ground at the same time. Gravity would pull both bullets toward the Earth at a constant rate (32 ft/sec2.) Since both were enacted upon from the same six foot height, both would reach the ground at the same time.

Question #3

A plane is flying at a rate of 500 mph. A rifle is mounted outside of the plane and has a muzzle velocity of 500 mph. When the rifle is fired does the bullet leave the gun seeing that they are both (the bullet and the plane) flying at the same rate?

First, ask yourself this. If you are in the same plane, that is traveling 500 mph, and you jump straight into the air, do you go flying backward at 500 mph? You would answer, “Of course not! What a ridiculous question!” However, we hesitate when asked something similar. The speed of anything within or mounted to an object traveling at a certain speed is relative to the speed of the object. If you are within a plane traveling at 500 mph then you are also traveling at 500 mph. If a rifle is mounted on a plane going 500 mph then it is also traveling at 500 mph. The bullet would leave the gun at precisely the same muzzle velocity, that it would, if the gun were sitting on the ground.

25 thoughts on “I Shot a Rifle into the Air…”

  1. The first two answers aren’t accurate. A bullet fired straight up would come back down at the same speed if the surface of the Earth was a vacuum, but wind resistance on a falling object sets a terminal velocity at which the accelerating force of gravity is exactly countered by the decelerating force of wind resistance. I don’t know the terminal velocity of a bullet off hand, and it would be dependent on whether the bullet was tumbling or spiraling as it does out of a rifled barrel, but in either case it is much slower than the muzzle velocity of a rifle. In summary, a falling bullet can be lethal, but it won’t be falling the same speed it was fired unless it’s fired in a vacuum.

    The second suffers from the same nit-picky problem. On a flat surface with even gravity downwards a bullet fired horizontally and a bullet dropped with hit the ground at the same time, but the curvature of the Earth means that a bullet fired from the gun would have to fall slightly more than the dropped bullet. The difference lies in the fact that you can’t do anything “horizontally” on a sphere, only tangentially.

  2. thanks for the comment, of course if there is wind and some other obstacles that will change the speed.

    But please do not say it is not accurate, it is 100% accurate information I had to ask few engineer friends to make sure…

  3. Interesting blog and a great read. So are you saying this is all true if you neglect air resistence and all factors that might affect it?

  4. Yeah. The answer to the first question is only true if you ignore any atmosphere at all. I dislike this answer because it is likely to confuse laypersons. In earth atmosphere, the bullet would hit the ground orders of magnitude slower than it left the gun.

  5. @Anonymous Coward

    Thanks for your insight but I assume the readers will look at the situation before getting into the problem. Atmosphere will of course bring some changes, imagine if there is a tornado.

    Common sense, i guess..

  6. There doesn’t need to be a tornado. Assuming that there is any atmosphere at all, even completely stationary air, the bullet would not reach the ground at the same speed at which it was fired upward. As has been already said, there is such a thing as terminal velocity, where the force from air resistance (friction, if you will) is equal to the force from gravity. Terminal velocity is much slower than muzzle velocity.

  7. Q-1
    Yes, The answer is accurate. If we assume the effect of the wind and air resistance is neglegible ( very reasonable assumption ), the bullet will regain the same velocity when arriving back to same place.
    Q-2
    The answer is right theoritically.But we must take into the account the fact that there is a huge difference of velocities of bullets. So we can not neglect air ressistance.So fired bullet arrives to earth bit late.
    Q-3
    The answer is correct but explanation is not.
    The bullet leaves the gun 500 mph relative to the plane but not relative to the Earth.

  8. I don’t mean to sound pretentious, but it became obvious after reading your explanations and further comments thus: you should definitely leave answers to questions about physics to those who understand. Your answers are accurate but misleading, normally assuming totally textbook explanations without taking into account reality.

    You can’t disallow atmosphere as if there’s no atmosphere you aren’t under the conditions of gravity and then there’s no such thing as firing a gun “up”, meaning it can’t come “down”. Also, making the assumptions that we use earth’s gravity and earth’s atmosphere, and also accounting for variable wind resistance, the bullet will only accelerate at 9.8m/s and will reach terminal velocity (depending on the weight and aerodynamics of the bullet) at a speed which may be painful to be hit with but wouldn’t be deadly unless it was an incredibly lucky shot. Your real inaccuracy lies in the statement that the bullet would fall back to the ground as fast as it was fired, which it wouldn’t and is why you shouldn’t have said anything in the first place.

    Also, speaking as a person who has a degree in science, I boldly speak out against the complete reliability of “friends”, as I have been in classes with tons of “friends” who I know for a fact don’t understand a lick of what they say.

  9. I would suggest this post is removed until all of the assumptions are correctly stated. I am an engineer and there is an argument with every “answer” you give.

    1 – The bullet would arrive slower than when it exited the gun. However, not necessarily at it’s terminal velocity. Terminal velocity happens when the force of gravity equals the force of the drag on the object. The bullet will not travel at the same speed as it left because it always experiences drag. The first commenter is about 20% right. Anonymous coward is 100% correct. He isn’t referencing wind or a tornado. He(or she) is referencing the molecules in air. The same thing you feel against your arm when you stick it out a window of a moving car.

    2 – This could be true. The vertical acceleration of the bullets will be identical if they have the same orientation to the ground. The reason it is most likely not true is because the bullet will acquire stability in the air and may actually product a lifting force depending on it’s orientation and rotation. This question is tough to answer, but it is easier to just break it up in to components. The horizontal speed of a object has a negligible effect on the vertical acceleration of the object.

    3 – This is most correct. The bullet, at the instant it leaves the barrel and before it has a chance to be acted upon by the air will be traveling 500 mph (in your example) faster than the plane.

  10. Thank you for deep insight AJ.

    I wrote what I found in my research. And I won’t be removing this piece of work as I would like to see more comments and views thus helping me understand the matter better.

    I gave it a try, but with more comments and feedbacks I can may be produce another copy.

  11. I think Stumblerz should continue with these articles not because he is completely right but it brings different people on this forum who enter their intelligent or not so intelligent thoughts into their comments.
    It would have been difficult for a layman like me to understand what he was talking about had not you all entered your comments and suggestions on to this section helping me understand what you are saying. So i think this should go on and we can finally find out what actually would happen in this case.

  12. Thanks for the comment, Ben. For the record, I am a he.

    Getting back to the matter at hand, I did a little number crunching with the aid of NASA’s online terminal velocity calculator and some data on the coefficient of drag for various shapes and objects and determined that, at the most, a bullet shaped object traveling straight down with no spin would hit the ground between four and five meters per second, or 1.5 percent the muzzle velocity of some rifles.

    The calculation is rather basic, though, and in reality it might be as much as 10 meters per second, but still nowhere near the muzzle velocity.

  13. One thing that I think it is important to remember for question 1 is that the bullet has velocity that propels it straight up thanks to the gun. Once the bullet reaches its apex it starts back down at 0 velocity and builds to its terminal velocity. This happens without the gun, which propels the bullet beyond the normal effect of gravity for a short period of time on the way up. The bullet has no way to speed back up beyond the terminal velocity you get with free falling objects. The bullet now is no different than the bullet dropped in question 2. The chances of it doing enough damage to kill is very small with only gravity as its fuel. This is the same reason why a coin dropped off of a high rise building won’t kill.

    By the way, in your example the bullet would go back into the barrel of the gun not hit the shooter, if, as you said, no other forces applied.

  14. @Ben

    I know something about the author of this post. That he has a degree in engineering also and that he researched this particular article with an electrical engineer (his father.) Therefore saying you are an engineer is not impressive. All of th answers are correct. Unfortunately, the assumptions are purposefully not stated to cause dicussion. Yes numbers 1 and 2 only occur in a vacuum. They are theoretically correct. Number 3 is correct, and it is assumed that we are talking about speed relative to the plane. Any idiot can see that.

  15. when flying a small air plane, the difference between a warm, muggy day and a cool day is the difference between night and day…..would imagine the same would be true of the bullet.

    would also depend on the proximinty to the north pole, composition of the bullet, etc. as it might be drug off course slightly.

    then there is the spin of the planet, so the person would move slightly, and if a duck was flying over head or something….that would be cool.

  16. A bullet fired straight up COULD kill, the terminal velocity for a bullet fired from a gun with a rifled barrel would be higher than for one dropped from any height, this is becasue it is stabilized by its spinning, so it points straight down and has much less wind resistance. A large rifle fired straight up, or as close to straight up as possible, would have a good chance to kill someone IF it managed to hit them.

  17. @ everyone who said terminal velocity was the only problem with #1. Another reason it is wrong is that it would also experience the Coriolis effect, unless the gun is aligned with the axis of rotation of the earth (or decently close such that the effect isn’t so great). Due to the rotation of the earth, while the bullet is in the air, the entire earth will rotate below it and hence, if the gun is pointed directly upwards, the bullet would not follow a perfect up/down trajectory (with reference to the shooter) and depending on the power of the gun, may land a number of feet away from the shooter.

  18. Oh, my god. This is so inane, inaccurate and confusing.

    Your answers are outright wrong, misleading or don’t even answer the question you asked! (Question 3: You asked if the bullet and plane are traveling the same speed after firing the gun. The answer is NO, the bullet is traveling 500mph FASTER than the plane at the moment it leaves the gun, but rapidly decelerates) You also inanely discount variables that, as they would affect the original question you asked in a major sense, sometimes to a greater extent than gravity itself. If you’re going to talk about a perfect vacuum, you have to say you fire the gun in a perfect vacuum. But you discount air resistance, when the very title of this post is “I shot a rifle into the *AIR*.”

    Question 2 is not convoluted. Question 2 is one of the most basic questions in examining physics of motion, examining the exceedingly simple principle that acceleration on one axis of movement is unaffected by velocity along a different axis.

    Oh, and gravity as you use it is not a constant. Gravity is a function of mass and distance. What you seem to think is a constant, 9.8 meters per second per second, is actually an estimate/average of the acceleration at sea level caused by gravity; a LOCAL gravitational field. If you’re going to say that air resistance gets tossed out because it is not constant, then you need to toss out gravity, too, because gravitational acceleration at the equator is approximately 9.78 meters per second per second, but 9.83 meters per second per second at the poles: not constant. And as you rise through the atmosphere, this force lessens. So understand the difference between a useful approximation for working out problems and a true constant, like pi or the speed of light (or the actual universal gravitational constant).

    I’m not saying using 9.8 m/sec^2 is wrong in figuring out a problem like this. It’s totally fine and educational to use that figure. But I am saying that if you’re going to discard something as important to this question as air resistance because it is variable, then you’re operating on a completely arbitrary dismissal, probably because one seems a lot harder to figure out. And it’s pretty obvious you struggle with things that are hard.

    Get another hobby, stop confusing and misleading people.

  19. @areReady

    thank you for your insight, the piece was written after research. You are welcome to add your views.

  20. @AJ

    Yeah, but with the second answer, the local topography of the land is going to have far greater impact on when the bullet hits the ground than the curvature of the earth.

  21. @AJ
    Completely agree AJ, wind resistance should never have been ignored.

    There’s a problem working out the terminal velocity of a bullet, however. Bullets aren’t actually designed to function the same on the way back down as they would on the way up, and this causes the following problem:

    Which part of the bullet is heavier? Unless you’re working with specialised ammunition, the bullet is generally all one metal (usually lead). Given they are designed for reduced drag, the tip is smaller than the base. Therefore, the base will be the heaviest part of the bullet. This will result in the bullet falling base first, not nose first, which (given the base is flat) will likely cause the bullet to tumble most of the way down, increasing drag even more.

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