# Fired a bullet upwards, can it fall down and kill me?

I know that if something is thrown up with a velocity v, it comes down with the same velocity as long as its motion faces no resistance. So is it possible for me to fire a bullet and be killed if it drops down on me directly? Assuming there is no air resistance.

• Yes this is entirely possible – Jaywalker Feb 3 '16 at 9:41
• How big is the bullet? :-) . <-- seriously, consider the extremes. A tiny bullet will not have enough kinetic energy to hurt you; a gigantic bullet fired at a microscopic speed might crush you but that's gravity, not kinetic energy. – Carl Witthoft Feb 3 '16 at 15:02
• Just to note, "assuming there is no air resistance" makes this completely unrealistic, since the only reason the bullet would travel at a different speed upon landing than it does out of the muzzle is energy loss due to air resistance. – Asher Feb 3 '16 at 20:53
• "Fired a bullet upwards, can it fall down and kill me? Need answer quickly!" – Michael Feb 23 '16 at 18:49

Yes the bullets can fall down and injure or kill you. In fact in countries were celebratory gun firing is possible people are often injured by falling projectiles.

Shooting straight up is less dangerous than at an angle because the terminal velocity is much lower than the muzzle velocity of the projectile.

When shooting at an angle some of the horizontal motion tends to be conserved making the bullets velocity when it falls back substantially higher.

https://en.m.wikipedia.org/wiki/Celebratory_gunfire

Now how fast would the bullet hit you when coming straigt down? Assuming it reached terminal velocity, its speed would depend on its mass and surface area.

$v_{terminal}=\sqrt{2mg/C \rho A}$

The density and drag coefficient of air are assumed to be constant at 1.29 $kg/m^3$ and 0.5 resepectively. If the bullet weighs 30 grams* and has a classic caliber of 9 mm, then the terminal velocity would be

$v_{terminal}=\sqrt{2*0.03*9.18/0.5*1.29* 0.009^2\pi}$

$=58.9 ms^{-1}$

Even a weak a very standard rifle has a muzzle velocity twice that value as seen here:

https://en.wikipedia.org/wiki/Muzzle_velocity

*averaged mass of bullets as given by the source: http://hypertextbook.com/facts/2000/ShantayArmstrong.shtml

• I agree that a bullet shot straight up is less dangerous to people than a bullet shot at an acute angle, but not because "some of the horizontal motion tends to be conserved" in the latter case. It's because the bullet spends less time in the air before hitting someone, so air resistance has less time to slow it down. – Brionius Feb 3 '16 at 11:45
• @Brionius I don't think air resistance alone would have enough time to slow a bullet down in either case. But gravity does bring a vertical bullet to a stop, while a horizontal bullet will have kept most of its horizontal momentum. – T. Verron Feb 3 '16 at 16:09
• @T.Verron but gravity also accelerates the bullet on the way down. In the absence of air resistance, a bullet that has fallen back down after being fired vertically would have a speed equal to the muzzle velocity; conservation of energy. – Brionius Feb 3 '16 at 17:02
• @Brionius but there IS air resistance. Anyhow there are multiple sources that confirm that the horizontal momentum barely changes. – Jaywalker Feb 3 '16 at 18:22
• @Jaywalker Gravity plays absolutely, positively, no role in reducing the downfalling velocity of a bullet. The principle of conservation of energy indicates that whatever deceleration gravity provides on the way up, it provides exactly equal acceleration on the way down. The reduced lethality of downfalling bullets is due to air resistance, and has absolutely nothing to do with gravity. – Brionius Feb 3 '16 at 18:37

There is always air resistance, unless you are in space. If there was no air resistance, a bullet would land at the same speed it was shot at.

On Earth, a spent bullet is rarely lethal. In big wars (like World War II) it was common for soldiers to get hit by spent bullets. Normally they will hit you and fall away, causing just a bruise,

An unlucky hit could kill a person. For example, if a falling bullet hit a person directly in their head and it was a hard jacketed bullet and the point happened to contact the skull first, it might penetrate and kill. Usually this will not happen, either because it will hit at an angle, or the bullet (which tumbles) makes contact on its side, not the point...

• Yeah I guess it's extremely unlikely to happen in real life cases. Won't have that much of an impact. – Aman Thakkar Feb 3 '16 at 12:53
• This is wrong, as documented cases show. "Rarely hits someone on the head" is not the same as "Rarely lethal." – Carl Witthoft Feb 3 '16 at 15:00
• @CarlWitthoft No, YOU are wrong. Most of the "documented" cases are not people being hit by spent bullets, but by stray non-ballistic shots. Cases in which a person has been killed by an "on top of the head" shot, like Shannon Smith (1999) are very rare. – Ambrose Swasey Feb 3 '16 at 15:35
• There's not a lot of precise info on the energy (kinetic) required to pierce the skull. Averaging a few semi-reliable papers I found, a 0.22 to 0.33 round will do so at around 1000J . Estimates of terminal velocity range from 50 to 100 m/s, which implies a required mass of 0.5 to 0.2 kg -- and one would imagine that a sharp-pointed mass of 0.5kg would penetrate, or at least damage, the skull at quite lower speeds. So I'll accept that only a small percentage of bullets which hit someone on the head cause serious damage. – Carl Witthoft Feb 3 '16 at 15:56

## protected by Qmechanic♦Apr 14 '16 at 13:42

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