The Dropping Bullet?

Question

O.K., here's an easy one...

At the same time that a high-speed bullet is fired horizontally from a rifle, another bullet is simply dropped from the same height. Which bullet strikes the ground first?

a) The dropped bullet
b) The fired bullet
c) Both strike at the same time

I'm glad that eople are not simply reading the question, but reading and then stopping. Even turn off the computer. Even put it away and THINK about the question.

If you are given a hammer with which to drive nails at the age of three you may think to yourself, "OK, nice." But if you are given a hard rock with which to drive nails at the age of three, and at the age of four you are given a hammer, you think to yourself, 'What a marvelous invention!" You see, you can't really appreciate the solution until you first appreciate the problem.

What are the problems of physics? How to calculate things? Yes -- but much more. The most important problem in physics is perception, how to conjure mental images, how to separate the non-essentials from the essentials and get to the heart of a problem. HOW TO ASK YOURSELF QUESTIONS. Very often these questions have little to do with calcualtions and have simply yes or no answers. Does a heavy object dropped at the same time and from the...

same height as a light object strike the earth first? Does the observed speed of a moving object depend on the observer's speed? Dpes a particle exist or not? Does a fringe pattern exist or not? These qualitative questions are the most vital questions in physics.

With most of the questions you will find many answers don't turn out as you first expect. Does this mean you ahve no sense for physics? Not at all. Most questions were deliberately written to illustrate those aspects of physics which seem contrary to casual surmise. Revising ideas, even in the privacy of your own mind, is not painless work. But in doing so you will revisit some of the problems that haunted the minds of Archimedes, Galileo, Newton, Maxwell, and Einstein. The physics you cover in my questions in hours took them centuries to master. I hope your hours of thinking on these questions will be a rewarding experinece and enjoyable! :)

The answer is c. Too bad I can't give a "Best Answerer" to everyone who chose it. There are some really great thoughts that I very much enjoyed reading. Valder, while off on this qquestion, anticipated my next. Remo and Linlyons always have great stuff to consider. So, here's my explanation....

The answer is c because both bullets fall the same vertical distance with the same downward acceleration (I know this on a practical level as a former Navy aviator). They therefore strike the ground at the same time (gravity does not as one answerer stated, take a holiday on moving objects).

This problem can be better understood by resolving the motion of the fired bullet into two parts; a horizontal component that doesn't change because no horizontal force acts on it (except for air resistance), and a vertical component that accelerates at g (italics) and is independent of its horizontal component of motion.

Or we can look at this another way....

If the rifle is pointed upward above the horizontal then the dropped bullet will strike the ground first. If on the other hand, the rifle is pointed downward toward the ground, the fired bullet obviously wins. Somewhere between up and down, there will be a draw -- and that's when the rifle is horizontal.

And there's another and quite different way to look at this. Suppose the ground accelerated upward, rather then the bullets downward. Can you see that the outcome would be the same?

Answer 1

The answer, as I feel, is C if the speed of the bullet is lower than the speed needed to turn it in to a satellite which will never fall back, provided nothing resists it's motion (eg. air drag or any object), in which case the dropped bullet will reach the ground first. My explanation is also based on the assumption that the height is not comparable to the radius of the planet in which case the curvature may make the situation complex. It is the same as given by many above.
All this implies that a normal gun fires a bullet horizontally from a raised coordinate with respect to a horizontal surface which exerts a force that is proportional to the mass of the subject.

The fired bullet was fired horizontally. and the dropped bullet, too, had been just dropped and given no velocity as seen from the ground.
The force of gravity acts on both of them in same vertical direction with the same effect. Why should the force affect a velocity that has no component in it's direction?
The only thing that it can do is create a new velocity in the direction of it's application hence making the initial horizontal velocity immaterial up to certain limits.

Answer 2

A.

First, the earth has a curve. If the speeding bullet goes 1/4 mile before it lands (reasonable assumption), it will have an extra 1/2 inch to drop. Drop = R*(1-1/cos(theta)) where theta is based on the arc of travel. R is the earth radius assumed to be 4000 miles.

(To make it easy, let's assume that the bullet is fired at either the North or South pole, because if not, you'd have to throw in some sort'a directional coefficient to deal with the earth's rotation. E.g. if fired in a direction opposite the rotation of the earth, the effective acceleration of gravity would increase due to decrease in centripetal acceleration caused by the earth's rotation. Note: At the equator the speed of a bullet is comparable to the rotational speed of the earth which would make the bullet fired in a vacuum and against the earth's rotation fall faster than the bullet simply dropped)

Second, the speeding bullet will create some aerodynamic lift as it starts to drop that is resistive to its fall. It acts as a symmetrical airfoil. This probably has a greater effect than the earth's curvature.

>>>>>>>>>>>>>>>
Linlyons (an answerer below),

I'm assuming that the bullet continues to be oriented horizontal. Even though they aren't a wing, they are still an aerodynamic body and as soon as they begin to drop just a little as a result of gravity, you will create an angle of attack (direction of velocity is different than the axis of the bullet). It will cause some lift.

I also just remembered that bullets spin which I would think would help keep them oriented. Acts like a 'flywheel.' So I just googled "bullet spin." There were some posts at site below that seemed to confirm both spin and aerodynamics. http://www.physicsforums.com/archive/index.php/t-17721.html

Best regards ...............I'm off to Starbucks now

.....................Eh Linlyons, I'm back

You raise interesting thoughts well beyond my personal knowledge, but let take a stab anyhow:

1. That site I noted above gave numbers that bullets have about 3/4rd expected drop compared with gravity. That's a pretty big drop: a lot more drop than a toy glider or any sort of airplane. It means the the lift forces on the bullet are about 1/4 g.

(Although, I expect it might be more on the order of 1/10g -- this is because most rifles aim slightly high so that the bullet will be even with the scope at 200m and the person explaining everything might not have taken that into account, so I ran out the numbers myself taking the high point to be at 100m and 0.1 secs into the bullets flight and I got 1/10 g).

2. v^2 is a marvelous thing. Lift is based on it and bullets go fast. This means that a small angle of attack can generate some pretty big forces.

3. What is happening is that you have two sets of forces, one is the gyro rotation which helps keep the horizontal attitude. The second is the aerodynamic forces, which, when you have an angle of attack will (1) create lift and (2) and will cause the bullet to 'pitch' forward so that it assumes the most aerodynamic orientation (i.e., going straight in to the relative wind direction)

But to cause the bullet to pitch forward and become streamline, you need a lift force centered behind the cg of the bullet. This means that any missile type projectile will have some angle of attack and will generate some lift force just to get its attitude pointing in the right direction. Ergo, any missile type projectile, because of the lift it must experience to maintain proper attitude, will fall more slowly than if just dropped. It may be very little lift, but it will be something.

The gyro force will keep the bullet from pitching foward too fast so that you get an even greater angle of attack and more lift. Found this site on naval weapons which is generally supportive: http://www.fas.org/man/dod-101/navy/docs/es310/ballstic/Ballstic.htm .

You would also want a fairly small angle of attack and fairly small lift forces on a projectile because otherwise you would get a lot of drift and accuracy problems.

4. I see what you're saying about corkscrewing. That could be a problem. I don't think you'd see much precession, but if you did, it would be pretty tight and self correcting. It may also cause some drift to one side (depending on rotation). I think the first article I cited above mentioned that problem if you have too much spin.

-I've been thinking about precession more. G is down. That means that, if there is an angle of attack and spin, the gyroscopic force would cause it to drift (i.e. begin pointing) towards one side thereby giving that side an angle of attack. This would cause lift on that side of the bullet which would straighten the bullet or at least cause the cork screwing to be minimal. Self correcting. Comments?

-An additional thought. Even if it corkscrewed, the bullet would still need 'lift' to change the attitude axis it is rotatating about so that the attitude follows the projectile path. In other words, summing everything as it goes around its corkscrew, the bullet would still have a net upward lift component. Make sences. Any holes?

*Just found a site that actually mentions precession and lift. You were right about the corkscrewing. They even have a graph showing it. Go down the "Some Caveats" section of the article. http://www.frfrogspad.com/extbal.htm

5. Turbulent flow might be a problem, but that would affect accuracy. My understanding from my education over the past two days is that bullets are (unfortunately) fairly accurate.

Answer 3

C) They both would hit the ground at the same time because gravity is acting on both of them equally. Even though the fired bullet is traveling horizontally gravity still exerts the same amount of force on it as it does on the dropped bullet.

Answer 4

A, of course. your average bullet fired from a good rifle can travel up to a mile. a tall man staning at full height just dropping a bullet will only have 6ft for the bullet to fall. now, even considering that the fired bullet is travelling 700mph or so, and the dropped at 9.8m/sec squared...it wouldn't take the dropped bullet even a tenth of a second, whereas the fired would take about twice that to make it the hypothetical mile, and since velocity can counteracct gravity for a time........unless you're talking about in a vaccuum, where velocity and gravity are nix'd

Answer 5

C) They both strike at the same time.
They both are subject to the same constant acceleration from gravity.

Answer 6

C. Gravity still works.

Answer 7

C) both strike at the same time.

Answer 8

a

Answer 9

C.