Hypothetical situation question

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SC4006

New member
I've been thinking about a hypothetical situation involving firearms in my head for a little while, and I just can't quite seem to come to a conclusion.

Lets say you have a hypothetical train that travels in a straight line at exactly 1000 feet per second. Lets also say you have a gun that shoots a bullet at exactly 1000 fps every shot. Logic would tell me that if it were fired in the same direction that the train is traveling while on the train, then the bullet would have a velocity of the sum of it's original velocity plus the train's velocity, so 2000 fps. My question is, what happens to the bullet if fired in the opposite direction that the train is traveling? I looked the question up on google, and according to howstuffworks.com, anyone observing the bullet fired in the opposite direction of travel while on the train would indeed see it as traveling 1000 fps, but for someone observing while not on the train it would seem like the bullet is stationary. I just can't totally make sense of that, as the expanding gases would always have to push the bullet out at 1000 fps no matter what, right? I would like to hear your thoughts.
 
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sandmansans

New member
You want to read Einsteins theory of relativity. I'm not proficient enough in physics to fully explain it to you, but there are some well explained articles out there that take your hypothesis on a trainbut replace the gun with light. I'll try to see if I can find one.

Sent from my SM-N910V using Tapatalk
 
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olddav

New member
The bullet exists the barrel at 1000fps as it should and moves away from the muzzle and you (relationally) at 1000fps, but in relation to the ground it is stationary. There is a lot more to it but them are the basics.
 
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JohnKSa

Administrator
...the expanding gases would always have to push the bullet out at 1000 fps no matter what, right?
Click to expand...
Right. Relative to the GUN.

The bullet will leave the barrel of the gun moving 1000fps away from the gun.

If the gun is stationary then the bullet will be moving 1000fps when it leaves the barrel.

If the gun is moving at 1000fps, in the same direction that the barrel is pointing, then the bullet will be travelling at 2000fps when it leaves the barrel.

If the gun is moving at 1000fps, in the opposite direction that the bullet will leave the muzzle, then the bullet will be traveling at 0 fps when it exits the barrel.

In ALL the cases the bullet will move away from the gun at 1000fps when it leaves the muzzle. Its velocity relative to the gun's velocity will differ by 1000fps.

Here's an easily visualized experiment. They had troubles getting the velocities exactly matched, but they finally got it right.
https://www.youtube.com/watch?v=DXkmc2p_Zio

If you really want to bend your mind, try to figure out what happens when the gun is moving at 1000fps and is fired at right angles to the direction of travel of the gun.

The answer is that from the standpoint of a non-moving observer, the bullet will travel at a 45 degree angle that splits the 90 degree angle between the gun's aiming point and the gun's direction of travel. The velocity of the bullet from a non-moving observer's perspective will be about 1414fps.

From the standpoint of the shooter, the bullet will move away at 1000fps.

From the bullet's perspective, it will see itself moving away from the gun at 1000fps, it will see the aiming point moving away to the side at 1000fps and when it looks down at the ground it will see itself moving forward at about 1414fps.
 
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cecILL

New member
For the stationary observer, the bullet would seem to appear out of nowhere and drop straight to the ground.
 
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mehavey

New member
For anyone on the train, in either direction, it would move away from him at 1,000fps

For anyone standing still/next to the train:
- 2,000fps going out the train front.
- 0 (zero/drop to the ground) going out the back
 
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gunnre

New member
Very interesting brain-tease this morn. I'm five of those four bad at math. Appreciate Johnska' s explaination simplified. While reading my minds video track playing the Road Runner and Coyote cartoon. Thank you for the Sunday morn entertainment.
 
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g.willikers

New member
Iz Zimple.
Velocity in one direction is considered a positive number.
Velocity in the other direction is considered a negative number.
Just add them up.
 
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DaleA

New member
You want to read Einsteins theory of relativity.
Click to expand...
Or NOT

I am not a fisisyst nor have I played one on TV but I suspect as long as we are talking about speeds of thousands of feet per second we can stick with Newtonian stuff...Einstein's relativity is a whole 'nother dimension. (Maybe literally another dimension...maybe several dimensions...like I said I'm not, well you know.)

Goodness, we haven't had one of these type discussions in a while...I'm getting my popcorn out...

Oh, and if we get tired of trains can we move it into the vacuum of SPACE and talk about shooting between satellites in different orbits?
 
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SC4006

New member
Iz Zimple.
Velocity in one direction is considered a positive number.
Velocity in the other direction is considered a negative number.
Just add them up.
Click to expand...

I guess it really is just that simple. I just couldn't quite wrap my head around the bullet seemingly just fall out of the barrel as witnessed by a stationary observer, but it definitely makes sense. Also thanks for your explanation JohnKSa. Actually seeing a similar situation happen in the mythbusters video is quite fascinating.
 
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carguychris

New member
JohnKSa said:
If you really want to bend your mind, try to figure out what happens when the gun is moving at 1000fps and is fired at right angles to the direction of travel of the gun.

The answer is that from the standpoint of a non-moving observer, the bullet will travel at a 45 degree angle that splits the 90 degree angle between the gun's aiming point and the gun's direction of travel. The velocity of the bullet from a non-moving observer's perspective will be about 1414fps.

From the standpoint of the shooter, the bullet will move away at 1000fps.

From the bullet's perspective, it will see itself moving away from the gun at 1000fps, it will see the aiming point moving away to the side at 1000fps and when it looks down at the ground it will see itself moving forward at about 1414fps.
Click to expand...
...and just to make things a little more complex, assuming that the bullet is fired on the planet Earth rather than in a vacuum, it will experience a 1,000 fps crosswind. This will affect both the path of the bullet and the amount of drop, which will be different out of each side of the train, and will change depending on whether the gun barrel has a left-hand or right-hand twist.

http://www.exteriorballistics.com/ebexplained/articles/article2.pdf

As an interesting historical twist, these factors help explain why it was so hard during WWII to effectively defend against enemy fighters using a bomber's on-board machine guns. Consider that the guns were often mounted in rotating turrets and could transit up an down; depending on which direction the turret was pointing, the gunner could be firing into a 250± mph headwind, a 250± tailwind, or a 250± mph crosswind from either direction, at an angle up or down, at a target moving across the gunner's field of vision at 300± mph, often in the opposite direction of the bomber, since German fighter pilots quickly learned that attacking roughly head-on minimized the time that their airplanes would present a target. The math involved in calculating the correct aiming point boggles the mind, and was effectively impossible to solve quickly enough using the technology of the time.* This explains why there were relatively few hits, and why the bombers proved to be very vulnerable to fighter attack until they were provided with long-range fighter escorts.

*This situation got better with the advent of digital computers, on-board radar for range measurement, and longer-ranged 20mm cannon, but air-to-air and particularly surface-to-air missiles quickly made on-board gun defense quixotic. This is why the USAF's B-52 bombers had their tail guns removed decades ago.
 
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TailGator

New member
I just couldn't quite wrap my head around the bullet seemingly just fall out of the barrel as witnessed by a stationary observer
Click to expand...

Part of your problem is that you are trying to imagine a train going 680 miles per hour, which isn't part of anyone's experience.

Einstein actually wrote a charming little book explaining relativity to the common man using examples and thought experiments. It is still in print.
 
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olddav

New member
Quick question.
Would the flight time of the bullet differ if fired forward (with the trains momentum) as opposed to rearward (opposite its momentum)?
 
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FlyFish

New member
If by "flight time" you mean the elapsed time between the bullet exiting the barrel and striking the ground, that's independent of the bullet velocity (ignoring minor effects of air resistance, earth curvature, etc.). For the same reason, if you drop a bullet from your hand at the same time as a similar bullet is fired from a gun aimed exactly horizontally (and with hand and muzzle at the same height), both strike the ground at the same time.
 
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RickB

New member
If you were on the train and fired the bullet in the direction of the train's travel - straight ahead - wouldn't the bullet "come back" and hit you?
The bullet would immediately experience the drag of 2000fps flight and the train would catch it, but before the bullet hits the ground?
 
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FlyFish

New member
The situation is somewhat similar to the test pilot story that carguychris linked to. The bullet leaves the muzzle at 2000 fps but immediately starts to slow due to air resistance. The train continues on at a constant speed of 1000 fps. If the bullet wasn't also falling, the train would eventually catch up to it, but of course it is falling and my gut tells me that, if fired horizontally, it would hit the ground before the train catches it - but I have no math to back that up. Perhaps someone with a ballistics program could plug in a typical BC for the bullet and provide a more definitive answer.
 
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