Physics question

[Valley Oak]

Does a bullet come back down to the ground with the same velocity as when it went straight up in the air when fired from a gun?

This scenario precludes ricochet, lost bullets, or bullets fired horizontally or vertically.

[handy]

Does a bullet come back down to the ground with the same velocity as when it went straight up in the air when fired from a gun?

This scenario precludes ricochet, lost bullets, or bullets fired horizontally or vertically.

The short answer is yes.

The long answer is that the projectile travels OUTward from center of gravity, decelerating from muzzle velocity to zero due to gravity. It then accelerates under gravity as it returns INward toward center of gravity.

The arc, no matter how narrow or wide at the base, is always parabolic.

In a Universe of spiralinear vectors, 'up' and 'down' are meaningless. As is the (purely imaginary) 'straight' line.

[Cheingrand]

I appreciate a concise and scientific answer. I am a Social Scientist and don't have a physics/math background to look at such questions. But it seems to me that a projectile fired with a black powder charge will accellerate upwards at a speed determined by the size of the charge, the rifling of the barrel, and the weight of the projectile. This may be noted as muzzle velocity and is a variable dependent on the above. When this projectile attains its apex, it will fall back to earth at a predictible speed. Are you saying that it will fall at the same speed as the muzzle velocity at which it was sent skyward?


The short answer is yes.

The long answer is that the projectile travels OUTward from center of gravity, decelerating from muzzle velocity to zero due to gravity. It then accelerates under gravity as it returns INward toward center of gravity.

The arc, no matter how narrow or wide at the base, is always parabolic.

In a Universe of spiralinear vectors, 'up' and 'down' are meaningless. As is the (purely imaginary) 'straight' line.

[notsomuch]

Outside the world of homework questions, there are some folks who will get quite specific:

bullet shot hits ground at the same time as a bullet that is dropped. - Topic Powered by Social Strata (https://community.discovery.com/eve/forums/a/tpc/f/9701967776/m/97619996201)

This part from page 2 of that thread probably addresses the specific question better, since:


This scenario precludes ricochet, lost bullets, or bullets fired horizontally or vertically.


Say you fire a gun at 91 degrees from the ground (just 1 degree HIGHER than parallel to the ground), the fired bullet would reach the ground AFTER the dropped bullet, because again, it much spend some time in upward motion, while the dropped only concentrates on going down. In an opposite case, firing the bullet at 89 degrees (just 1 degree BELOW parallel), the fired bullet would reach the ground BEFORE the dropped bullet, because it was given a little bit more assistance to go downward having being shot only minutely lower than parallel.

Although of course this question is about the velocity and not the time it takes, still - if a bullet fired vertically is different that should tell you something if it's also not horizontal.

[donaldmc]

I appreciate a concise and scientific answer. I am a Social Scientist and don't have a physics/math background to look at such questions. But it seems to me that a projectile fired with a black powder charge will accellerate upwards at a speed determined by the size of the charge, the rifling of the barrel, and the weight of the projectile. This may be noted as muzzle velocity and is a variable dependent on the above. When this projectile attains its apex, it will fall back to earth at a predictible speed. Are you saying that it will fall at the same speed as the muzzle velocity at which it was sent skyward?


As objects fall through our atmosphere attracted by the earth's gravatational force they attain a terminal velocity due to atmospheric friction which would slow the falling bullet to a velocity slightly less than the original muzzle velocity.

[marko]

I don't have the exact numbers for either the projectile going upward or falling downward but I'd guess the speed fired from the gun, the speed as it rises to the highest point, and the speed dropping to earth are NOT 'the same' (that is, the fastest speed leaving the gun upwardly and the fastest speed dropping to earth are NOT the same). Reason(s): the speed of the bullet on its upward path would be determined by the type of gun, type of ammo (and there are a LOT of variables in the ammo--weight of bullet, powder type and quantity, shape/style of bullet. It would have a muzzle velocity (the speed it's going as it leaves the barrel), and I know that muzzle velocity varies greatly from bullet to bullet, gun to gun. AND I think the speed of the bullet (after it's reached its maximum altitude and begins to fall to earth) is governed by gravity and wind/air resistance as it falls, with the concept of 'terminal velocity' coming into play along the path down; not sure exactly of the physics, but I think there's a maximum speed beyond which it will not accelerate any faster. What say, all you real physicists out there in Waccoland?


I appreciate a concise and scientific answer. I am a Social Scientist and don't have a physics/math background to look at such questions. But it seems to me that a projectile fired with a black powder charge will accellerate upwards at a speed determined by the size of the charge, the rifling of the barrel, and the weight of the projectile. This may be noted as muzzle velocity and is a variable dependent on the above. When this projectile attains its apex, it will fall back to earth at a predictible speed. Are you saying that it will fall at the same speed as the muzzle velocity at which it was sent skyward?

[handy]

For the experiment, charge size, rifling and projectile weight are approximately irrelevant. Muzzle velocity IS peak speed. No further acceleration takes place once the projectile leaves the barrel. Deceleration begins immediately (32 ft./sec/sec) and speed falls to zero (vertical) at apex. Falling inward, the projectile accelerates at one gravity (32 ft./sec/sec) until impact.

Terminal velocity due to air resistance acts on both the outbound and inbound leg, so the effect washes out as negligible.

A larger charge will result in a higher arc, but the lengths of both the outbound and inbound legs of the (always) parabolic arc remain equal.





I appreciate a concise and scientific answer. I am a Social Scientist and don't have a physics/math background to look at such questions. But it seems to me that a projectile fired with a black powder charge will accellerate upwards at a speed determined by the size of the charge, the rifling of the barrel, and the weight of the projectile. This may be noted as muzzle velocity and is a variable dependent on the above. When this projectile attains its apex, it will fall back to earth at a predictible speed. Are you saying that it will fall at the same speed as the muzzle velocity at which it was sent skyward?

[handy]

I don't have the exact numbers for either the projectile going upward or falling downward but I'd guess the speed fired from the gun, the speed as it rises to the highest point, and the speed dropping to earth are NOT 'the same' (that is, the fastest speed leaving the gun upwardly and the fastest speed dropping to earth are NOT the same).

Your guess would be wrong.


Reason(s): the speed of the bullet on its upward path would be determined by the type of gun, type of ammo (and there are a LOT of variables in the ammo--weight of bullet, powder type and quantity, shape/style of bullet.

ALL of these variables are eliminated when you choose THAT bullet and THAT gun.


AND I think the speed of the bullet (after it's reached its maximum altitude and begins to fall to earth) is governed by gravity and wind/air resistance as it falls, with the concept of 'terminal velocity' coming into play along the path down; not sure exactly of the physics, but I think there's a maximum speed beyond which it will not accelerate any faster.

In my limited experience skydiving, yes, I found that terminal velocity is variable depending on body shape. Falling spread-eagled, 'flat and stable', terminal velocity is approximately 120 mph. Bringing arms in to your sides, feet together and toes pointed, 'max track' will reduce air resistance and boost terminal velocity to over 200 mph.

Given smoothness and density (mass:volume) of a bullet, air resistance will be a vanishingly small component of the equation.

[Valley Oak]

I apologize for the confusion inherent in my question and I must make a crucial clarification.

When I said "vertical," I was thinking in terms of a slant, not straight up or down. For example, if you are looking at a square drawn on a piece of paper with ink or pencil, and then draw an internal line going from one corner (any of its four corners) and proceed to draw it straight to its opposite corner, THAT is what I meant by vertical.

But I forgot that the word, vertical, is also used to mean straight up and down, which is what has confused the good people who have invested their time on this thread.

I hope this clears things up.

Furthermore, in my opinion, it is impossible for a bullet to travel as quickly with gravity (in its return to the ground) as it did when fired straight up in the air with a powder charge propelling it.

Any thoughts?

[Zeno Swijtink]

Your guess would be wrong.


Your assertion that his guess is wrong is wrong. That's my (tentative) assertion.

[handy]

Your assertion that his guess is wrong is wrong. :):

And you can quote laws of physics to back this opinion?

[Zeno Swijtink]

And you can quote laws of physics to back this opinion?

The Law of Conservation of Energy (included in the first law of thermodynamics) and the second law of thermodynamics, which states that the entropy of an isolated macroscopic system never decreases.

Assume a pistol on an unmovable platform fires a bullet against a gravitational field with constant gravity and uniform direction, in an atmosphere with constant density. (These assumptions model the situation pretty close.)

On the outward bound some of the kinetic energy is converted into heat (both of the bullet and of the air molecules in the bullets path), some into potential energy (in the gravitational field).

On the inward bound the heat energy is not converted back into kinetic energy as the bullet is pulled back by the gravitational force (this would violate the second law) and the potential energy is converted back into kinetic energy.

In fact also on the inward bound some of the potential energy is converted into heat, both of the bullet and of the air molecules in the bullet's path.

So when the bullet falls back in the barrel it has less kinetic energy.

[Tars]

Heh heh...nice response, Zeno.

[handy]

Okay. You're absolutely right.

That said, I think you're nitpicking the fuzziness of the edge of the envelope, while ignoring the message. The projectile will be just as lethal coming in as going out. If you are on the incoming end (which is the only criterion that matters), you will not be noticing any trace slowing due to air friction.


The Law of Conservation of Energy (included in the first law of thermodynamics) and the second law of thermodynamics, which states that the entropy of an isolated macroscopic system never decreases.

Assume a pistol on an unmovable platform fires a bullet against a gravitational field with constant gravity and uniform direction, in an atmosphere with constant density. (These assumptions model the situation pretty close.)

On the outward bound some of the kinetic energy is converted into heat (both of the bullet and of the air molecules in the bullets path), some into potential energy (in the gravitational field).

On the inward bound the heat energy is not converted back into kinetic energy as the bullet is pulled back by the gravitational force (this would violate the second law) and the potential energy is converted back into kinetic energy.

In fact also on the inward bound some of the potential energy is converted into heat, both of the bullet and of the air molecules in the bullet's path.

So when the bullet falls back in the barrel it has less kinetic energy.

[podfish]

good point. For all practical purposes it should, but there will be an 'error factor' that's not going to be easily determined. Here's an easy way to visualize it. Imagine you shoot a ball of feathers at a huge velocity (magic feathers that won't disintegrate...). In a vacuum, they'd do a nice ballistic path and the terminal velocity would match. In an environment with a lot of air resistance, they'd slow down extremely quickly and would softly float to the ground. Also, there's the rotation of the earth to consider....


.. fired with a black powder charge will accellerate upwards at ... muzzle velocity ... it will fall back to earth at a predictible speed. Are you saying that it will fall at the same speed as the muzzle velocity at which it was sent skyward?

["Mad" Miles]

Edward,

You weren't firing a gun into the sky at midnight on New Year's were you? This ain't Tikrit!!

Out here in the wild's of F'ville I was negligbly tempted to do so myself, but resisted the notion. Even though I know, at least vaguely, which direction would result in reentry in a fairly unpopulated area. Just didn't feel like talking to the Sheriff's at 12:45 a.m....

Vertical means "straight up and down". I think you meant to say, "at an upward angle".

Bullets dropping back to earth do occasionally kill people. Perhaps without the velocity they had when leaving the barrel, but with sufficient velocity to kill. I recall reading that this occurs occasionally in some Middle Eastern urban areas during celebratory occasions.


Podfish,

Ball of feathers? In atmosphere the resistence of a ball of feathers and a lead slug are quite different. Even indissolvable feathers.


Where are the physics majors!? Nice general elucidation Zeno, but theory isn't proof.

What I vaguely know as a layman (Just shootin' off my keyboard here...); There is air resistance at all times. (Very few if any bullets are fired in a vacuum!)

What slows down the bullet as it rises are both wind resistance and the pull of gravity, but more importantly the loss of momentum over time and distance. As it falls back to earth, wind resistance is still a factor. What accelerates it as it falls is momentum provided by gravity x distance x weight and shape of the bullet.

What provides momentum as it goes up is muzzle and firepower velocity (already touched on in previous replies by others) relative to the weight and airodynamics of the projectile (minus air resistance, including side and head winds. Humidity, altitude, and other atmospheric conditions probably have some small effect as well.)

I'm sure there's a physics formula for this. But I don't know it and haven't done an internet search to find out.


Not firing any actual projectiles of a physical nature at the moment,


"Mad" Miles

:burngrnbounce:

[Valley Oak]

I'm still finding it hard to believe.

Let's suppose that I'm riding a hot air balloon at the highest possible altitude. And from that height I DROP a bullet so that it can only travel toward the ground at the greatest velocity that gravity can give it.

Questions:
1. Would the velocity of the bullet falling to the ground (understanding that it can be no faster than what gravity gives it) be as fast as when a person fires the same bullet straight up into the air?

2. Really now? Can the velocity of a bullet, garnered only from gravity, kill a person? I have serious doubts.

I can understand how a ricochet bullet or a bullet fired horizontally could easily kill a person. I have no doubts there at all.

I'll tell you a story about a real event that took place in Denmark in the 1990s while my family was still living there. There was a wedding being celebrated by immigrants (can't remember if they were Turkish, Afghani, or some other nationality) and one of the guests pulled out his gun and fired several shots up at the ceiling. Tragically, the ceiling was made out of concrete and all of the bullets ricochet with such force that they killed some of the people present, including the bride.

This I can understand.

But I cannot understand that gravity alone can give such a small piece of metal the same deadly force.

Anyone care to respond?

Thanks,

Edward



Edward,

You weren't firing a gun into the sky at midnight on New Year's were you? This ain't Tikrit!!

Out here in the wild's of F'ville I was negligbly tempted to do so myself, but resisted the notion. Even though I know, at least vaguely, which direction would result in reentry in a fairly unpopulated area. Just didn't feel like talking to the Sheriff's at 12:45 a.m....

Vertical means "straight up and down". I think you meant to say, "at an upward angle".

Bullets dropping back to earth do occasionally kill people. Perhaps without the velocity they had when leaving the barrel, but with sufficient velocity to kill. I recall reading that this occurs occasionally in some Middle Eastern urban areas during celebratory occasions.


Podfish,

Ball of feathers? In atmosphere the resistence of a ball of feathers and a lead slug are quite different. Even indissolvable feathers.


Where are the physics majors!? Nice general elucidation Zeno, but theory isn't proof.

What I vaguely know as a layman (Just shootin' off my keyboard here...); There is air resistance at all times. (Very few if any bullets are fired in a vacuum!)

What slows down the bullet as it rises are both wind resistance and the pull of gravity, but more importantly the loss of momentum over time and distance. As it falls back to earth, wind resistance is still a factor. What accelerates it as it falls is momentum provided by gravity x distance x weight and shape of the bullet.

What provides momentum as it goes up is muzzle and firepower velocity (already touched on in previous replies by others) relative to the weight and airodynamics of the projectile (minus air resistance, including side and head winds. Humidity, altitude, and other atmospheric conditions probably have some small effect as well.)

I'm sure there's a physics formula for this. But I don't know it and haven't done an internet search to find out.


Not firing any actual projectiles of a physical nature at the moment,


"Mad" Miles

:burngrnbounce:

["Mad" Miles]

OK Ev'body,

Curiosity got the best of me and after a ten minute web browsle (is this a word?) I came up with this:

https://www.answerbag.com/q_view/275 (https://www.answerbag.com/q_view/275)

It doesn't directly answer Edward's question, because it presumes a "vertical" launch. But the answers seem to be informed, when not quixotically tongue in cheek.

Podfish,

Thanks for your private reply. I was reading too quickly and your response prompted me to go back and reread the last few posts. I did not read you carefully enough. Ditto for Zeno.

May I humbly suggest that your response would be more elucidative if it had been made publicly?

(Before I spell checked elucidative, I'd come up with "elucitive". Not a word, but I propose its addition to the English language!)

I can understand the desire to not appear to trivially bicker publicly (if that was what motivated you to reply privately?) but I've a thick skin, I assure you I can take it. And if I find I can't, rest assured, I'll let you know!

And Zeno, loved the quip at the end of your able response!

Out for now,

"Mad" Miles

:burngrnbounce:


Edward,

I missed your response when I was editing this second one of mine. Check out the link I've provided. You should find your answer.

From what I understand, the return velocity would not be the same as the muzzle velocity. But if the distance of the drop was sufficient, to allow maximum acceleration, the bullet might have enough speed and mass to kill.

This is a variation on the "penny dropped from the Empire State Building" (or is it the Burg Dubai?) question.

The difference being that a lead shaped charge has more mass and possible aerodynamic qualities than a flat disc of copper.

"M"M

[handy]

Thanks for staying on point. And asking the important question.
Mad Miles wrote:
Edward,

You weren't firing a gun into the sky at midnight on New Year's were you? This ain't Tikrit!!




From what I understand, the return velocity would not be the same as the muzzle velocity. But if the distance of the drop was sufficient, to allow maximum acceleration, the bullet might have enough speed and mass to kill.

Distance of the drop = distance of the rise.
Gravity is the governing constant. Gravity sucks. The rate of deceleration outbound is the same as the rate of acceleration inbound. Each additional second of fall is moving 32 feet per second faster than it was in the last second. This adds up in a hurry. Air resistance on a small, heavy, smooth object is negligible.


This is a variation on the "penny dropped from the Empire State Building" (or is it the Burg Dubai?) question.

Love it! A new standard.:wink: Speed of a penny from 1/2 mile out?


The difference being that a lead shaped charge has more mass and possible aerodynamic qualities than a flat disc of copper.

"M"M[/QUOTE]

Yes. And the denser and more aerodynamic the falling body, the more negligible the effects of air resistance.

In Michigan's Upper Peninsula, back around early-mid 60s, some hunters came across a skeleton in the woods. Shot dead some years prior, he still had his rifle in his lap. The 30.06 slug removed from the tree above him didn't come from his rifle (different calibre). Some students at Michigan Tech at Houghton were invited to try to solve the ballistics involved. They concluded that it had been fired into the air from over 2-1/2 miles away.

Hell, even a box of .22 shorts carries a warning of danger: 1 mile range.

[Valley Oak]

I followed Miles' link and the following answer, amongst many others, is the one I liked the most. It does not answer my question "perfectly" but it comes pretty damn close!

Another person said "I would personally take a bullet up to the height it should reach when fired, and then drop it base first and see what happens." This adds a tiny bit more information but the other answer, below, is much more complete.

Also, I noticed there is an overwhelming, irresistible urge for quite a number of folks to express serious concern and even admonishment for even asking this question in the first place for fear that someone might actually go out and do this, hurting people. This preoccupation was so pervasive that it leads me to believe that the true answer can never be found because human passions are far too powerful to overcome.

Perhaps the real answer is based on agnosticism: the idea of a bullet being shot out of a gun, straight into the air and then falling back to earth is too much for the human mind to be able to successfully ponder. If anyone ever did serious research, using the scientific method, and succeeded in finding the answer, they probably kept this information safely away from the public for fear that people would start going out shooting their guns into the air, causing a lot of harm to others. Kind of like "top secret," classified, or highly sensitive information.

Look at it this way, we humans were smart enough (at least some of us) to successfully land a man on the moon in 1969, 41 years ago. However, we don't know the answer of velocity, trajectory, return, etc, of a tiny rocket we call a bullet, doing the same thing the Apollo spacecraft did back in the 60s.

That is the true answer to the question; it is a purely unscientific one because we are all incapable of dispassionate, scientific study and discourse in order to find the "real" solution, whatever that is.

I can see it now, front page headlines on the Holy Grail of the bullet question answered. Then, as millions of Americans are sipping their morning coffee, reading the bullet solution, they suddenly have a blank expression overtake their faces (by the millions, coast to coast). And like zombies, without speech, automatically but slowly go get their guns, load them, walk outside their homes and places of work, and start shooting all of their rounds into the air, causing the worst killing spree in world history with tens of millions of dead Americans within hours.

Keeping the bullet question a mystery is a matter of serious national security. If the true answer is ever revealed, then the terrorists win. I hope have not sparked the attention of the authorities for having started this thread. I think I might best delete it as a patriotic act. After all, ignorance is patriotism. Human nature is too pathetic to ever responsibly know the truth. People prefer to continue believing in the bible and keeping their experience within an infantile fantasy world. Who are we to question this (or anything else for that matter).

Edward

Below is my preferred feedback on the bullet question:

************
I think that I need a clarification here. A couple of people have already failed to read the entire answer and down rated me because the obviously misunderstood what I was stating. I am not saying that firing a gun in the air is not potentially deadly. I am addressing narrow case of shooting straight up. The Mythbusters actually tested this. Their methodology was sound and showed that a bullet fired STRAIGHT up will not come back down at a velocity that is even sufficient to break skin. So, please read THE ENTIRE ANSWER befor you rate it or leave a comment stating that I don't know what I am writing about.
************

No one here has gotten the right answer. A bullet fired straight up will not come back down with enough force to do any serious injury. This is because as it goes up its spin will slow and it will begin to tumble on the way back down. This tumble will prevent the bullet from achieving a dangerous velocity on the way back down.

However, very few people are able to fire a bullet straight up. If you don't get the bullet going straight up, then it follows a parabolic trajectory. If this happens then the the bullet can maintain its stability and a significant portion of its muzzle velocity. Thus it can come back down with enough speed to actually do serious damage. This is what actually happens in cases where people or things are injured by bullets shot into the air. So, it is still a bad idea.

I got this information from the Mythbusters. They actually tested this by dropping bullets in a vertical wind tunnel and placing guns in mounts that would hold them vertical. All of their test shows that a bullet fired straight up will not return to earth with sufficient velocity to cause serious harm.

If you stop and think about it for a minute this should actually make sense. How many people are killed by pea sized hail? Hale would probably have a higher terminal velocity than a bullet because it doesn't matter if it tumbles. The nearly spherical shape of the hail will have the same air resistance no matter what face is leading. It takes pretty large hailstones to really do damage.

So, simply falling out of the sky, a bullet will not pick up enough speed to be dangerous. It has to be on a parabolic course (which will be the case the vast majority of the time a person fires a gun into the air) in order to be dangerous.


OK Ev'body,

Curiosity got the best of me and after a ten minute web browsle (is this a word?) I came up with this:

https://www.answerbag.com/q_view/275 (https://www.answerbag.com/q_view/275)

It doesn't directly answer Edward's question, because it presumes a "vertical" launch. But the answers seem to be informed, when not quixotically tongue in cheek.

Podfish,

Thanks for your private reply. I was reading too quickly and your response prompted me to go back and reread the last few posts. I did not read you carefully enough. Ditto for Zeno.

May I humbly suggest that your response would be more elucidative if it had been made publicly?

(Before I spell checked elucidative, I'd come up with "elucitive". Not a word, but I propose its addition to the English language!)

I can understand the desire to not appear to trivially bicker publicly (if that was what motivated you to reply privately?) but I've a thick skin, I assure you I can take it. And if I find I can't, rest assured, I'll let you know!

And Zeno, loved the quip at the end of your able response!

Out for now,

"Mad" Miles

:burngrnbounce:


Edward,

I missed your response when I was editing this second one of mine. Check out the link I've provided. You should find your answer.

From what I understand, the return velocity would not be the same as the muzzle velocity. But if the distance of the drop was sufficient, to allow maximum acceleration, the bullet might have enough speed and mass to kill.

This is a variation on the "penny dropped from the Empire State Building" (or is it the Burg Dubai?) question.

The difference being that a lead shaped charge has more mass and possible aerodynamic qualities than a flat disc of copper.

"M"M

[Zeno Swijtink]

Okay. You're absolutely right.

That said, I think you're nitpicking the fuzziness of the edge of the envelope, while ignoring the message. The projectile will be just as lethal coming in as going out. If you are on the incoming end (which is the only criterion that matters), you will not be noticing any trace slowing due to air friction.

Can you provide the detailed physics of that opinion?

[Zeno Swijtink]

Can you provide the detailed physics of that opinion?

Hint: use the formulas about Drag, a concept from fluid dynamics, for the terminal velocity vt of a falling object (https://en.wikipedia.org/wiki/Drag_(physics)) and choose as Drag Coefficient 0.04 (https://en.wikipedia.org/wiki/Drag_coefficient).

For instance, a (dead) small bird cannot fall faster ~ 20 m/s.

Then consider the concept of Momentum = Mass x Velocity, and of Sectional Density = Weight /Diameter^2. For an explanation see

How Hard Does It Hit? (https://www.thudscave.com/npaa/articles/howhard.htm)

My guess is that one cannot be killed by a .357 magnum thrown from the Empire State Building: it just has too small a mass (125 grains) and too small a terminal velocity.

handy, you need to do the work!

[dandss1]

the question really is....can you catch it in your teeth??