# Q & A: Stopping a bullet in mid-air

Most recent answer: 01/23/2013
Q:
Although your website clearly states that a bullet shot straight up will not come down at the same speed, I have talked to many people that say that the air resistance on a bullet is so little that it doe not even slow it down. Is there a way to prove your point mathematically? Thank you.
- Steve Garner (age 25)
Arizona State University, Phx AZ
A:
Steve -

All objects feel air resistance. I am guessing the quotes you've heard about air resistance being insignificant for a bullet refer to a bullet shot horizontally at something. In this case, the bullet reaches its target and stops so quickly that there is not enough time for air resistance to have much of an effect on it.

However, if you shoot a bullet straight up, it will take quite a long time for it to fall again. When the bullet reaches the top of its trajectory and starts to fall again, the speed that it gains is due only to gravity. At some speed, the force of air resistance (which depends on velocity) will equal the force of gravity (which does not depend on velocity). This is what's referred to as 'terminal velocity.' All falling objects have a terminal velocity. The smaller the object is, the higher the terminal velocity. For a bullet, one estimate that I have read for terminal velocity is around 300 ft/sec (about 200 mph). Since that's a lot slower than a bullet leaves a gun nozzle, it seems that the air resistance really will have a big effect on the speed of the falling bullet.

-Tamara

(published on 10/22/2007)

## Follow-Up #1: Falling bullets hurt but usually not lethal

Q:
Where did you find a gun with a nozzle? Every gun I have seen has a muzzle. I have never heard of anyone speaking about nozzle vilosity.

By the way I work with a gun nut who swears that the bullet cannot fall straight back down and kill someone. I believe that at your estimated speed of 200 mph a 150 grain bullet would easily penetrate a human skull.
- Les (age 56)
Helena Mt
A:
Yeah, ’nozzle’ sounds like part of a big water pistol. Small goof.

On the terminal velocity, a quick google produced a reference to some Army tests: "the bullet return velocity was about 300 f.p.s. For the 150 gr. bullet this corresponds to an energy of 30 foot pounds. Earlier the Army had determined that, on the average, it required 60 foot pounds of energy to produce a disabling wound. Based on this information, a falling 150 gr. service bullet would not be lethal, although it could produce a serious wound." So it seems that Tamara's estimate of the terminal velocity was indeed the accepted value (for this standard bullet) and that your friend is right that it would not usually produce a fatal wound.

Mike W.

(published on 10/22/2007)

## Follow-Up #2: relative motion

Q:
This has been around some time but I can't get my head aroud it. If a train travelled through a station at 100mph and a person shot an arrow down a carriage at 100mph and the arrow exited an open door at the end of the carriage, would the people standing on the platform see a static arrow? I say that the arrow would be stationary - others say different. Thanks
- Peter (age 65)
St. Ives, Cornwall, UK
A:
You're right.

Mike W.

(published on 01/23/2013)

## Follow-Up #3: Air resistance and bullets

Q:
In regards to the question regarding the speed of a bullet when it is shot up and coming back down. On a day without wind, would not the air resistance be the same going up as it is coming back down? This would make the speed on the way down equal the speed going up.
- Andy Grzywacz (age 27)
University of St. Francis, Joliet, IL
A:
Hi Andy,

Friction acts to dissipate energy and make objects that are rubbing against each other move in similar directions and speeds. In the case of a bullet being shot into stationary air, the air resistance pushes down on the bullet while the bullet is traveling upwards. At the top of the bullet's path, its speed is zero, although it is still accelerating towards the earth. At this top part, the air resistance force drops to zero because the bullet and the air are not moving with respect to each other. On the way down, the air resistance pushes against the bullet's direction of motion, in this case, pushing upwards, slowing the bullet down. If the air resistance force always pointed down, then it would slow the bullet on the way up and speed it up on the way down (just like gravity), and the two speeds would be more similar.

The bullet loses energy to air resistance both on the way up and the way down (try throwing a sheet of paper loosely wadded up into a ball as hard as you can straight up in the air and see how fast it hits the ground to see this effect).

Tom

(published on 10/22/2007)