Gravity/physics - a question

[RealityCheck]

Hang on. Let me get this question straight in my mind.

You are pointing a gun straight ahead of you on a totally straight surface. You fire the gun and at exactly the same moment drop a bullet from the same height to see which one will hit the floor first? Am I right about this?

If I am, then it seems to me that it is the bullet that you drop.

Although the effect of gravity is the same on both there is a fundamental difference between them. The bullet you've dropped has only one velocity: a downward one. The bullet however technically has two: a downward one but also a tremendous forward velocity.

It's like if you drop a piece of paper or throw a paper airplane. The piece of paper hits the floor first before the airplane (so long as you haven't fudged the plane design). Similarly if you have two identical (decent) paper airplanes and you let one just drop from shoulder height and throw the other from the shoulder then the one you dropped will hit the floor first.

The forward velocity of the fired bullet makes no difference. That doesn't help the bullet counteract the force of gravity, which is the ONLY force acting on both bullets after firing/dropping.

 

[Blackmarch]

I have a question about which my wife and I have been arguing, and I'd appreciate it if anyone of the many on these forums who know more about physics than I could answer it conclusively, along with an explanation as to why:

Imagine you are standing on a perfectly flat plain. In one hand, you hold a loaded, high-powered handgun. In the other hand you hold a bullet of the same type with which the handgun is loaded. Both hands are at the same height above the ground. You point the handgun exactly parallel to the ground and, at precisely the same time, pull the trigger and drop the bullet in your other hand.

The question: which bullet hits the ground first, the one you dropped or the one you fired?

if the gun is exactly level, the bullets started at the exact same height (and are BBS rather than bullets), on a perfectly flat infinite field with uniform gravity, and the air currents act upon both in the exact same manner.. then both bullets would strike the ground at the exact same time-
here is why; both have the exact same amount of downward force acting upon them without having any other force add or subtract to the downward force... a perfectly horizontal acceleration will not affect the downward force by itself in any way.

 

[Data]

Imagine a train that moves as fast as a bullet. When riding on this train, dropping a bullet will take x amount of time, weather the train is moving or not.

Excellent analogy, it explains the situation in a very understandable way.

I'd recommed this one, OP.

 

[Kripost]

I agree with every one here. Both will fall at the same rate.

I think part of it is psychological. I remember when doing archery, while shooting at a target 10 metres away, the trajectory seems rather flat, whereas for a target 90 metres away, the trajectory is very noticable. This is asuming the same bow is used, and the draw length is consistent. On the other hand, using a more powerful bow would cause arrows to move faster horizontally, and give less time for gravity to act on the arrow, and thus giving the illusion that gravity has a lesser effect on faster objects.

Also, it takes about 1 second for an object released from shoulder height to reach the floor. Bullets fired from guns are supposed to reach their targets in far less time. Guns for longer distance need to change elevation to adjust for distance, e.g. in sniper rifles.

 

[arunma]

Hang on. Let me get this question straight in my mind.

You are pointing a gun straight ahead of you on a totally straight surface. You fire the gun and at exactly the same moment drop a bullet from the same height to see which one will hit the floor first? Am I right about this?

If I am, then it seems to me that it is the bullet that you drop.

Although the effect of gravity is the same on both there is a fundamental difference between them. The bullet you've dropped has only one velocity: a downward one. The bullet however technically has two: a downward one but also a tremendous forward velocity.

It's like if you drop a piece of paper or throw a paper airplane. The piece of paper hits the floor first before the airplane (so long as you haven't fudged the plane design). Similarly if you have two identical (decent) paper airplanes and you let one just drop from shoulder height and throw the other from the shoulder then the one you dropped will hit the floor first.

As has already been mentioned, neglecting the effect of the air, the forward velocity of the bullet is completely irrelevant to its downward velocity. That's the remarkable thing about the decoupling of horizontal and vertical motion. Actually, it works no matter what reference frame you want. You could define "up" as sixty degrees from the vertical, and horizontal and vertical motion would still be decoupled (though now, every force would have a horizontal and vertical component).

Now about the paper airplanes. The reason this analogy doesn't yield the correct solution is because a paper airplane experiences lift. Because of the upward force on its wings, the net acceleration downward is not the same as for the piece of paper. A fundamental assumption in this problem is that all objects accelerate towards the earth at the same rate. Since this doesn't apply in the case of a paper airplane, that is a very different scenario.

 

[Blackmarch]

As has already been mentioned, neglecting the effect of the air, the forward velocity of the bullet is completely irrelevant to its downward velocity. That's the remarkable thing about the decoupling of horizontal and vertical motion. Actually, it works no matter what reference frame you want. You could define "up" as sixty degrees from the vertical, and horizontal and vertical motion would still be decoupled (though now, every force would have a horizontal and vertical component).

Now about the paper airplanes. The reason this analogy doesn't yield the correct solution is because a paper airplane experiences lift. Because of the upward force on its wings, the net acceleration downward is not the same as for the piece of paper. A fundamental assumption in this problem is that all objects accelerate towards the earth at the same rate. Since this doesn't apply in the case of a paper airplane, that is a very different scenario.

having two angular velcities will make an object faster- it will cover more distance.. but they will be at equal points on the vertical line.

hopefully this illustration will help.

see illustration.

 

[Telephone]

Imagine you are standing on a perfectly flat plain. In one hand, you hold a loaded, high-powered handgun. In the other hand you hold a bullet of the same type with which the handgun is loaded. Both hands are at the same height above the ground. You point the handgun exactly parallel to the ground and, at precisely the same time, pull the trigger and drop the bullet in your other hand.

The question: which bullet hits the ground first, the one you dropped or the one you fired?

I put all your information into a dynamics system.

No air, Flat infinite plain, consistent gravity, horizontal shot (high horizontal velocity) and a dropped (zero horizontal velocity) bullet.

+ plus two velocities between 'zero' and 'high'

 

[arunma]

having two angular velcities will make an object faster- it will cover more distance.. but they will be at equal points on the vertical line.

hopefully this illustration will help.

see illustration.

When you mention angular velocity, are you talking about rotation? I'm fairly certain that this would not influence linear motion (that is, unless the bullet spontaneously began spinning, which would steal energy from the linear motion).

Or are you talking about the bullets having multiple components of linear velocity? If two bullets have the same component of linear velocity in one direction, and one of the bullets has additional velocity along another direction, then of course that bullet will travel faster, since the magnitude of its velocity (the speed) will be higher. But here we are assuming that both bullets begin with the zero vertical velocity, and that one bullet begins with nonzero horizontal velocity.

By the way, I'm not sure I understood your diagram completely. Could you explain it further? Specifically, I'm wondering why you mention two forces (X and Y). Are you using these letters to represent gravity and air resistance? If so, then there should be three forces. Of course we have gravity. But we also have two air resistance forces. The horizontal and vertical air resistances are proportional to the square of the horizontal and vertical velocity And the two constants of proportionality depend on the cross-sectional surface areas along the directions of motion.

 

[Blackmarch]

When you mention angular velocity, are you talking about rotation? I'm fairly certain that this would not influence linear motion (that is, unless the bullet spontaneously began spinning, which would steal energy from the linear motion).

whoopssorry,
probably really ripped up the word-
2 seperate velocities that are aquired by 2 different forces, that act at different angles to each other.

Or are you talking about the bullets having multiple components of linear velocity? If two bullets have the same component of linear velocity in one direction, and one of the bullets has additional velocity along another direction, then of course that bullet will travel faster, since the magnitude of its velocity (the speed) will be higher. But here we are assuming that both bullets begin with the zero vertical velocity, and that one bullet begins with nonzero horizontal velocity.

yup that be it.

By the way, I'm not sure I understood your diagram completely. Could you explain it further? Specifically, I'm wondering why you mention two forces (X and Y). Are you using these letters to represent gravity and air resistance? If so, then there should be three forces. Of course we have gravity. But we also have two air resistance forces. The horizontal and vertical air resistances are proportional to the square of the horizontal and vertical velocity And the two constants of proportionality depend on the cross-sectional surface areas along the directions of motion.

X and Y represent two different but constant forces (or forces that act during the same timeframe), that act perpendicular to each other.- gravity would factor in as the main part of the y variable, while whatever other (such as forfce from propellant) force would factor in on the X variable. the variables basically would cover factors such like force, acceleration, and velocity, and resistance.

C is what would happen if those forces are combined

 

[arunma]

X and Y represent two different but constant forces (or forces that act during the same timeframe), that act perpendicular to each other.- gravity would factor in as the main part of the y variable, while whatever other (such as forfce from propellant) force would factor in on the X variable. the variables basically would cover factors such like force, acceleration, and velocity, and resistance.

C is what would happen if those forces are combined

Is one of those forces air resistance? If so, we must remember that this is not a constant force, becuase it is time-dependant.

 

[Blackmarch]

Is one of those forces air resistance? If so, we must remember that this is not a constant force, becuase it is time-dependant.

Generally no it isn't and you're right. However theoretically there could be a uniform environment which causes resistence