I can't show the work, but it's relatively easy to explain.

The forward velocity of an object does not affect the gravitational forces pulling on it. Therefore, two identical items dropped (or propelled) from the same height will hit the ground at the same time (if the experiment is in a vacuum and isn't effected by wind or lift or something of that sort).

What makes this counter-intuitive is probably partly the fact that we so rarely see, or hear of, a fired bullet hitting the ground before it hits some other object (ie. the target).

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mythbusters did this and in their eyes confirmed it.

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>> ^Skeeve:
I can't show the work, but it's relatively easy to explain.
The forward velocity of an object does not affect the gravitational forces pulling on it. Therefore, two identical items dropped (or propelled) from the same height will hit the ground at the same time (if the experiment is in a vacuum and isn't effected by wind or lift or something of that sort).
What makes this counter-intuitive is probably partly the fact that we so rarely see, or hear of, a fired bullet hitting the ground before it hits some other object (ie. the target).

This is precisely correct. The experiment assumes a vacuum, wherein there are no effects of air resistance. In a vacuum, all objects fall at the same speed regardless of mass, surface area, or, as is pertinent in this case, velocity perpendicular to the gravitational force. This is similar to why it is counter-intuitive that a bowling ball and a feather fall at the same speed: the experiment assumes a vacuum. In our experience, we consider a feather to be "light", falling slowly to the ground. But if there is no air resistance, the feather simply falls.


Skeeve's explanation of why this seems counter-intutive is also correct. The horizontal velocity of a bullet is so much greater than the vertical force of gravity that we don't perceive it as being affected by gravity at all, let alone the same as a bullet that is dropped, where the only force acting upon it is gravity.

The other reason it may seem counter intuitive is that the sights on a gun actually have the bullet traveling in an arc when firing at any sort of range. You're actually pointing slightly upward so the path the bullet follows will be like a football rather than a straight line to the target.

So compare that to someone throwing a football as hard as they can perfectly level to someone throwing a football in an upward arc. Which football will have more air time. Since your brain imagines the bullet traveling straight, rather than in an arc, your perception is skewed.

The point where most people get in trouble with, though is lift.
The experiment assumes a frictionless vacuum, but the question of the bullets involves air and one of the objects traveling at a high speed through it, meaning friction. This is where most people would assume the fired bullet would have some lift and would thus fall slower.

Anyway, the Mythbusters tackled this question as solecist mentioned, and it was oddly not sifted yet, so: http://videosift.com/video/Mythbusters-Fired-Bullet-Vs-Dropped-Bullet

It's exactly true if you ignore air, the curvature of the earth, relativity, time spent traversing the barrel of the gun, and the inaccuracy of the gun. The vertical component of acceleration, due to gravity, would be completely unaffected by its horizontal velocity.

The vertical component of friction could be larger or smaller when the bullet is shot out of the gun. I don't know. It shouldn't have lift because of symmetry.

That didn't seem counter-intuitive to me at all, assuming that the starting trajectory of the path is perfectly parallel to a perfectly flat surface beneath it.

Then again, the newtonian laws that one learns in High School or University starting physics classes tends to ignore lots of minor variables as mentioned above, like air resistance / friction. However, when you apply the simplified equations to real life experiments, it is usually quite amazing how accurate they are even having ignored those factors.

Your question about vertical friction changing depending on the horizontal speed of the bullet is an interesting one, jwray. It seems like there would be more exposure to molecules of air, so the friction would be slightly higher for a fast-moving bullet. On the other hand, being shot out of a gun would instantly overcome the stronger coefficient of resting friction versus the weaker coefficient of friction in motion. I agree that lift wouldn't be a factor due to symmetry. I guess I'm not surprised that any effect of friction is negligible in practical experimentation (ie Mythbusters), but I bet that you are correct that there is a slight difference between the two scenarios, but it is probably smaller than the effects of other, uncontrolled chaotic variables that differ between tests.

Actually this does not even assume a vacumm.

mythbusters proved this in a warehouse. under regular firing conditions:

http://www.youtube.com/watch?v=IAm1roCiVBA

Of course our brain has a hard time with this because no bullet is EVER fired at perfect horizontal under normal cercumstances... meaning it will have upward thrust when fired in most cases.

Here's another way of thinking about it...

A train passes a station, and as it does by a strange coincidence a passenger on the train and someone standing on the platform both drop their keys. They hit the ground at the same time, but the train passenger's has traveled a quarter of a mile through space before hitting the floor of the train, essentially creating an arc similar to that of a bullet.

>> ^schmawy:
Here's another way of thinking about it...
A train passes a station, and as it does by a strange coincidence a passenger on the train and someone standing on the platform both drop their keys. They hit the ground at the same time, but the train passenger's has traveled a quarter of a mile through space before hitting the floor of the train, essentially creating an arc similar to that of a bullet.


The problem with that analogy is that the air inside the cart is static, while from the perspective of the fired bullet, the air isn't. If the passenger was dropping his keys out of the train car's window, it would be more accurate

The Flying Spaghetti Monster is in the details.

hahaha all of you couch physicists. Yea, the only force acting on the bullet in the "y" component is gravity. It's the same for both bullets. In fact the acceleration due to gravity is the same for a bullet and a bowling ball or a semi-truck and a feather (in a vacuum of course).

Now the spin of the bullet, while stabilizing the bullets trajectory in the "x" direction, has very little affect over the bullets fall. That's probably a little more difficult to understand. Would probably need a course in fluids and aerodynamics to solve that.

The harder thing to understand would be if I told you that if you fired a bullet from a rooftop straight down to the ground, or you fired it at an upward angle, due to the conservation of energy, both bullets would have to be travelling at the same velocity magnitude when they hit the ground (although direction at impact would be different, obviously).

I love all you *nerds.

>> ^BURGNIEL:
Actually this does not even assume a vacumm.
This is exactly what I was going to say (except I was going to spell it vacuum). In a vacuum, everything falls at the same speed. Since both items being tested are the same size, weight, and shape, air resistance is nary a factor (however it would be different if it was a hammer versus a falcon feather). The only significant consideration here is the effect of wind on the fired bullet.

I think you need quite a tall rooftop for this to be true.

>> ^rottenseed:
The harder thing to understand would be if I told you that if you fired a bullet from a rooftop straight down to the ground, or you fired it at an upward angle, due to the conservation of energy, both bullets would have to be travelling at the same velocity magnitude when they hit the ground (although direction at impact would be different, obviously).

>> ^lucky760:
>> ^BURGNIEL:
Actually this does not even assume a vacumm.
This is exactly what I was going to say (except I was going to spell it vacuum). In a vacuum, everything falls at the same speed. Since both items being tested are the same size, weight, and shape, air resistance is nary a factor (however it would be different if it was a hammer versus a falcon feather). The only significant consideration here is the effect of wind on the fired bullet.


That's not really true (claims of air resistance not being a factor with regard to identical items moving vs. not moving). Throw an unpowered airplane at an appreciable speed and drop one straight down, and tell me that they'll hit at the same time.

I don't know enough about the aerodynamics of bullets to claim that they're going to get a lot of lift--in fact, the Mythbusters' test suggests that it's very small. But even that showed the dropped bullet hitting first. But large effects aren't just limited to airplanes, either. There are paintball guns that put backspin on the paintballs which give them lift and allows them to fly significantly further.

None of you show'd your work. I want equations! I want brains exploding over keyboards!

I love it how the first comment pretty much explained it, and yet everyone had a go afterwards.

>> ^oxdottir:
I think you need quite a tall rooftop for this to be true.
>> ^rottenseed:
The harder thing to understand would be if I told you that if you fired a bullet from a rooftop straight down to the ground, or you fired it at an upward angle, due to the conservation of energy, both bullets would have to be travelling at the same velocity magnitude when they hit the ground (although direction at impact would be different, obviously).


nope...be it an inch or 100 stories

Ug + KE(initial) = KE(final) for both scenarios the potential energy do to being on a roof and the velocity of the bullet leaving the gun are the same. As long as the mass of the bullets are the same, it'll land with the same velocity. (Trust me when I first heard that I did the brute force kinematic equations to solve this problem and it is in fact the same velocity.)

>> ^rottenseed:
>> ^oxdottir:
I think you need quite a tall rooftop for this to be true.
>> ^rottenseed:
The harder thing to understand would be if I told you that if you fired a bullet from a rooftop straight down to the ground, or you fired it at an upward angle, due to the conservation of energy, both bullets would have to be travelling at the same velocity magnitude when they hit the ground (although direction at impact would be different, obviously).


nope...be it an inch or 100 stories
Ug + KE(initial) = KE(final) for both scenarios the potential energy do to being on a roof and the velocity of the bullet leaving the gun are the same. As long as the mass of the bullets are the same, it'll land with the same velocity. (Trust me when I first heard that I did the brute force kinematic equations to solve this problem and it is in fact the same velocity.)

If I'm not mistaken, this also holds true for a bullet fired at a downward angle as well. (Since the upward angle bullet eventually becomes an identical downward angle bullet once it crosses back beyond the level from which it was fired.)
Of course, the confusing thing in the problem, if I understand correctly, is that velocity magnitude at impact is identical, while downward velocity will be less for the angled bullet.

when I took my firearms course I new that gravity was a constant and that this was true. My instructor was not very smart and did not believe me when I said this information.

Don't really understand why this is so counter intuitive to some people, it makes perfect sense to me.

Although, if you fire the bullet with enough force then it may never reach the ground. Assuming you don't live on a infinite plane with no atmosphere and consistent gravity ofc.

One thing I do wonder about, which is particularly pertinent to the result the mythbusters obtained, is compression.



They ultimately found that their two bullets struck the ground within a period shorter than the duration of a normal video frame. Assuming the bullet was successfully released level and at the same instant as their dropped bullet, would the slight increase in air density around the bullet, from compression when travelling at speed, explain the very slightly longer fall time? It appears that once you surpass 220mph, the compressive behaviors of gasses are no longer negligible.

Hmmm, quite a knowledgeable lot here. One thing that makes me want to dole out helmets is total disregard of a core scientific principal. Is the statement/observation true? Have you in fact been able to reproduce it for yourself? What happened to K.I.S.S?

In law, the judges go to great lengths to state; [don't tell me what he/she told you or what you think they knew. It's hearsay!]

In science, you first have to reproduce the phenomena, accounting for assumptions and all sorts of other things before suggesting a governing dynamic. Incidentally, this is what the whole Myth busters premise is. They reproduce then they explain!

..apples and oranges, powers of observation, listening skills, brain teaser, certainly NOT scientific, an experiment, observation or {i got a giggle with this one; something mythbusters 'debunked'. Yeah right}

The respondent was 'having his chain yanked'. He responded with the anticipated reply 'bollocks' (NOT bullocks but bollocks! on television! You see, it isn't word you want to use in polite company let alone be renown for bandying it about. Still dodgey to use this kind of language on terrestrial telly. [x-rated but you can google what it means across the pond].

Fry's reaction, 'i knew it' was in reference to the fact that it was the kind of response the gentleman would give.

RE: firing bullet up vs down. They will only have the same energy and therefore speed upon impact if there is no atmosphere to slow it down. Since the bullet fired up travels through much more atmosphere than the bullet fired down, its interaction with the air removes some of it's energy as heat, and it must have less energy upon impact. This is why things have terminal velocity. There's a point where they can't go any faster through the air due to gravity alone.

Sorry to sound a bit of an idiot, but if (and only if) this expiriment were to be assumed in a vacuum, would it not be possible to fire a gun as the bullet would require oxygen for the gunpowder to ignite?

Just askin'.

Extremely simple to explain. You guys are making it too difficult.

They both have the same vertical forces and same height, therefore they will hit the ground at the same time. Just draw free body diagrams. The only thing acting on both (in a vacuum) is gravity in the downward direction.

>> ^rottenseed:
>> ^oxdottir:
I think you need quite a tall rooftop for this to be true.
>> ^rottenseed:
The harder thing to understand would be if I told you that if you fired a bullet from a rooftop straight down to the ground, or you fired it at an upward angle, due to the conservation of energy, both bullets would have to be travelling at the same velocity magnitude when they hit the ground (although direction at impact would be different, obviously).


nope...be it an inch or 100 stories
Ug + KE(initial) = KE(final) for both scenarios the potential energy do to being on a roof and the velocity of the bullet leaving the gun are the same. As long as the mass of the bullets are the same, it'll land with the same velocity. (Trust me when I first heard that I did the brute force kinematic equations to solve this problem and it is in fact the same velocity.)




No. The longer a bullet is in flight, the more air resistance has affected it. The one fired at the ground would get there quicker, thereby retaining more of the energy imparted on it by the exploding gunpowder.

>> ^brycewi19:
Sorry to sound a bit of an idiot, but if (and only if) this expiriment were to be assumed in a vacuum, would it not be possible to fire a gun as the bullet would require oxygen for the gunpowder to ignite?
Just askin'.


Most modern "bullets" (cartridges to be precise, the bullet is just the projectile) have their oxidizer mixed in with the explosive. They can actually fire even underwater.

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