cracked butt
Member
I don't think so... the curvature of the earth works both ways.
If anything it would hit the ground slightly faster than when its fired because the gun was 5 1/2' off the ground to start with.
If I fired an arrow into the sky.....
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I don't think so... the curvature of the earth works both ways.
If anything it would hit the ground slightly faster than when its fired because the gun was 5 1/2' off the ground to start with.
I once had an instructor that had us figure out the velocity of a 22lr prejectile by firing it through a pair of paper plates spinning at a known rate of speed about 10 inches apart. All i remember is that you have to measure the distance (laterally) between the two holes and then do some math and you get the answer
I still cant figure out how he managed to bring a rifle into a lecture hall at the university and fire it into a bullet trap (i do believe that he used a CB cap though).
BluesBear
member
[voice=Bullwinkle J Moose] I shot an arrow,
Into the Sky.
It fell to Earth,
OWWWW... MY EYE! [/voice]
Into the Sky.
It fell to Earth,
OWWWW... MY EYE! [/voice]
horge
Member
Bluesbear!
Piney
Member
Since mathematics hadn’t been invented when I was in school I’ll have to claim ignorance. Anything more than 3 rocks and we were lost.
benEzra
Moderator Emeritus
Actually, in a vacuum, it would hit the earth's surface with the same velocity it started with (if it was fired from a point even with the surface).
Yes, the bullet has to "fall" a bit farther to get to the surface due to the earth's curvature. But the gravity vector also moves "behind" the bullet a little, so that the force is ALWAYS normal to the surface.
Another way to look at it is that on a perfectly spherical earth with uniform mass distribution, any two points the same distance from the center define identical gravitational potential energy. So a projectile gaining energy from gravity by going up and then coming back down to a point of the same elevation relative to the earth's center would violate the first law of thermodynamics.
Yes, the bullet has to "fall" a bit farther to get to the surface due to the earth's curvature. But the gravity vector also moves "behind" the bullet a little, so that the force is ALWAYS normal to the surface.
Another way to look at it is that on a perfectly spherical earth with uniform mass distribution, any two points the same distance from the center define identical gravitational potential energy. So a projectile gaining energy from gravity by going up and then coming back down to a point of the same elevation relative to the earth's center would violate the first law of thermodynamics.
What about the spin of the body from whence the projectile is fired?
In a vacuum if fired in a direction exactly opposite the direction of spin wouldn't that mean the relative impact velocity would be greater than the firing velocity kind of like two cars moving at 30 MPH hitting head on is the same as one car moving at 60 MPH hitting a stationary wall. Wouldn't the opposite be true?
In a vacuum if fired in a direction exactly opposite the direction of spin wouldn't that mean the relative impact velocity would be greater than the firing velocity kind of like two cars moving at 30 MPH hitting head on is the same as one car moving at 60 MPH hitting a stationary wall. Wouldn't the opposite be true?
NO...
But that's because the ball's motion already has the rotational velocity vector in it even while you are holding it.
In a vacuum that would also be true. So if in a vacuum a ball was tossed upward would it return to the same spot from which it was tossed? It seems likely.
Still my gut tells me that the spin of the body from which a projectile is launched must have some affect on the projectile's terminal velocity and point of impact.
OK all you physicists out there! Time to chime in...
I learned this as a child to apply in these situations:
I shot an arrow into the air
It fell to earth I knew not where
Until the next day, with rage profound
The man it fell on came around
And now I do not greatly care
To shoot more arrows into the air.
(I, not really learning this lesson, played many a game of archery golf where distance was a necessity. Some "holes" were a 1/2 mile long.)
I shot an arrow into the air
It fell to earth I knew not where
Until the next day, with rage profound
The man it fell on came around
And now I do not greatly care
To shoot more arrows into the air.
(I, not really learning this lesson, played many a game of archery golf where distance was a necessity. Some "holes" were a 1/2 mile long.)
Werewolf,
If you watched a shot from a point off the earth (not spinning) you would see a north/south shot curve in relation to YOU. However, if you looked at the launch point and angle versus the impact point, you would find that the shot DIDN'T curve. Although the shot DID curve in relation to you, the earth moved under the shot so that it landed in a straight line and at the proper angle from the starting point.
Just as the ball has the rotational velocity already applied when it is at rest in your hand, the bullet has the rotational velocity already applied when it is in the launcher.
If you watched a shot from a point off the earth (not spinning) you would see a north/south shot curve in relation to YOU. However, if you looked at the launch point and angle versus the impact point, you would find that the shot DIDN'T curve. Although the shot DID curve in relation to you, the earth moved under the shot so that it landed in a straight line and at the proper angle from the starting point.
Just as the ball has the rotational velocity already applied when it is at rest in your hand, the bullet has the rotational velocity already applied when it is in the launcher.
The system needs to be defined better.
For our purposes, we probably care most about what the impact looks like with relation to the target. Likewise, the shot will probably be defined with respect to the shooter.
In this situation, assuming a vacuum, the rotation matters greatly.
However, in a simpler situation, if we assume no rotation, then you can make accurate approximations by looking at the potential energy. Moving away from and towards the earth, the projectile is going to experience the same deceleration and acceleration: it will return to an equivalent starting point. Since the distance to the center of mass of the earth will be the same for both start and finish, and no loss of energy via drag etc in flight, the the initial speed will be equal to the final speed.
The exact path travelled is irrelevant.
benEzra
Moderator Emeritus
If you were moving linearly, yes. The earth's rotation can be approximated as linear movement over short distances, but it's really rotational, so you get into the Coriolis effect there. If you shoot due north, for example, the ground you're standing on is moving faster to the east than the ground where the bullet lands, so there's an apparent velocity gain. The bullet didn't gain any velocity, though, it just carried some of the extra equatorial velocity with it to the north (hence the apparent bending to the northeast).
Mikul,
"I do remember reading an article about idiots who shoot bullets into the air for celebration."
Guess we have that thing going on too.
Once, when I got to work, I found a spent bullet in the parking lot at work. It was in amazinly good condition. Looked to be about .30 cal. Riflling grooves on the side and only the nose was slightly bent were it hit pavement.
"I do remember reading an article about idiots who shoot bullets into the air for celebration."
Guess we have that thing going on too.
Once, when I got to work, I found a spent bullet in the parking lot at work. It was in amazinly good condition. Looked to be about .30 cal. Riflling grooves on the side and only the nose was slightly bent were it hit pavement.
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