Please settle an argument about ballistics. . .?

Question

A silly 'pub' argument.

A bullet fired from a gun exactly horizontally will hit the ground at exactly the same time as a bullet dropped from the same height as the gun barrel.

My friend maintains the force of gravity being the same on both objects they will hit the ground simultaneously.

I maintain that although this is true in a 'no atmosphere' situation, where there is an atmosphere the fired bullet is effectively 'flying'; and will hit the ground long after the dropped bullet.

Which of us is right?

Answer 1

1. Ignoring the curvature of the Earth
2. Assuming perfectly horizontal initial velocity
3. In no atmosphere
Then the only vertical force is gravity and so they will hit the ground at the same time.

However if there is an atmosphere,
1. The fired bullet does act as an aerofoil, because if you look at the shape of the bullet relative to the velocity vector of the air, the airflow vector is slightly from below as there is a forward and downward component of bullet velocity. This is why some ammunition has flatter trajectories than others.

2. If there is a side wind, the spinning of the bullet (assuming the barrel is rifled) introduces a vertical force, search for magnus force on the web. The boundary layer spins with the bullet so in a side wind, there may be an upward or downward force, depending on whether the wind is in the same direction or opposite to the direction of rotation of the top of the bullet.

In summary, as a pure school physics question, the answer is that they would hit the ground at the same time. The reality is that there are other factors at work that complicate the problem.

Answer 2

My students get this wrong all the time when I first pose this question. It is natural to assume that since the bullet that is fired will be in the air longer, because it is "flying", to use your word.

My answer: gravity begins to pull on the bullet fired the instant it leaves the gun. Therefore, it begins to fall the moment it leaves the gun. That is why someone who is firing a rifle at a target located a large distance away will aim a little higher to account for gravity.

Now, yes the bullet is traveling at a large speed. That only means that the bullet travels a large horizontal distance before it hits the ground. While the bullet is "flying" through the air, it is falling due to gravity. The "flying" part does not in any way turn gravity off! Once the bullet leaves the gun, there aren't any more forces propelling it forward. There are only two forces: gravity, and friction.

So, I always tell my students, the only difference between the fired bullet and the dropped bullet is the horizontal speed. Therefore, the fired bullet lands on the ground a tremendous distance away from the one that was just droppped.

Answer 3

You're friend is correct. Unless the bullet has an airfoil shape. A conical bullet will have zero lift if it's fired horizontally. Flight is caused by an airfoil creating lower pressure on top of wing or other surface, allowing upward acceleration. A normally shaped bullet or lead ball would hit the ground at the same time as a bullet dropped. I've done it with air cannons that were aimed at a target that was dropped from the ceiling as the bullet left it's chamber. You could vary the velocity all you want. At high speed, it impacted the target near the ceiling. At low speed, it would hit the target closer to the floor. It always hit the target.

Answer 4

Although the bullet may be "flying," there is no lift generated by the fact that the bullet is moving with great speed. When a bullet is fired from a gun, it is spun by the barrel. This spinning reduces the drag forces on the bullet, but does not generate even the slightest amoung of lift. This means that the bullet will travel further, but will hit the ground at the same time as the dropped bullet.

Answer 5

They should both hit the ground at the same time, BUT:

There is a "trick question" element you can use. As the Earth's surface is curved, the bullet moving in a horizontal line is TECHNICALLY on a trajectory away from parallel to the surface, and so would land slightly after the dropped bullet. Using this argument makes you kind of a dick, though.

Atmospheric drag has no bearing on the answer, the vertical component of it is the same for both bullets.

Answer 6

The Complete Idiot has the key: The bullet is not an airfoil. Why not? Looking from the side, an airfoil has a longer cross sectional path length on top than on bottom, and the difference in cross sectional paths causes the air velocity on top to be greater than on the bottom, which causes the pressure under the airfoil to be greater than the pressure above it. The pressure difference is what causes lift.
Now look at the bullet from the side. Not only is it symmetrical about its axis, but even if the slug wasn't perfectly symmetrical, it would be effectively symmetrical because it's spinning if the gun barrel has any rifling, as modern gun barrels do.
So, no airfoil, no extra lift. The bullets would indeed hit the ground at the same time.

Answer 7

Obviously, the fired bullet will hit the ground MUCH later than the bullet being dropped?!!!! How can this even be a debate??

A gun will be fired from shoulder height, so a bullet dropped from that height would fall at the rate of gravitational pull, and would hit the ground in about 1 seconds time.

A bullet fired from a gun is travelling at speeds of hundreds of meters per second, so will be airborne for far longer as it has far, far more kinetic energy than the other bullet, and is not technically "flying" but "carving" a passage through the air.

The kinetic energy of the fired bullet is initially greater than the pull of gravity.

I am a Military Sniper, I know!!

ps dont bother running, you'll only die tired

Answer 8

I forget the speed at which gravity puts on a falling object, but it is somewhere along 28.6 ft per second. For the fired bullet I will use my Ruger P90. Its a .45 caliber bullet travels out of the barrel at 1800 ft per second. So, lets say that the person who is firing the gun is six feet tall and the distance from the end of the barrel to the ground is 3 ft even. And, the person who is dropping the bullet holds it three feet from the ground. One will be traveling at 28.6 ft per second towards the ground. And, the other will be traveling at 1800 ft per second towards the ground. The fired bullet will hit the ground in .00166 seconds. The dropped bullet will hit the ground in .10489 seconds. much slower. The fired bullet will hit the ground much faster.

EDIT: scratch all my BS I misread your question. Horizontally vs. Vertically. hahah

Answer 9

You're sorta on the right track, but the wrong direction. A bullet is symmetrical and so there'd be no aerodynamic force perpendicular to the direction of travel. The only aero force is drag, which will slow it down but doesn't effect the gravity pulling it down. It should hit the ground at the same time as a dropped bullet.

Answer 10

sorry buddy but im pretty sure your friend is right. We went over this exact question in my physics class. the bullet is made of lead and it doesn't have wings...but it would be an interesting eperiment to do, I would think that if there is any weight to your theory of the "flying" bullet that it would still be only nanoseconds longer before it hit the ground. Another reason it may not get any lift is that bullets rotate through the air so if it lifted at one point it would fall quicker as it rotated 180d.

But hey, since its a pub debate you should just keep trying to convince him it will fly. tell him that since the earth is round that the bullet actually flys strait ahead and that is why it takes longer to hit.

good luck anyways...