Is Mythbusters' conclusion about bullet velocity accurate?

[jones106]

Hey guys, I just discovered this forum and have a question for yall. I am by no means an expert in physics. I've taken general physics I and II, but my physics knowledge stops there.

Hate to do this, but I've got to ask a question pertaining to a Mythbusters episode that I just saw. They were testing whether or not a bullet fired directly upward would be lethal when it reached the ground. They concluded from their experimental results that the bullet would not be lethal when it hit the ground.

From my limited knowledge of basic physics, I would think that the bullet would hit the ground with the same velocity and therefore the same kinetic energy and momentum as when it left the barrel of the gun. Here is my reasoning for this: The bullet leaves the barrel traveling at a certain velocity, and gravity slows it down at a constant rate of 9.8m/s/s. The bullet's kinetic energy is completely converted to potential energy when it reaches its maximum height. The potential energy of the bullet is then converted to kinetic energy as the bullet falls back to earth. So, when the bullet reaches the ground it should have the same kinetic energy, and thus momentum, and when it left the barrel of the gun. I would think that the bullet would be just as lethal as when it was originally fired.

Sorry for the long windedness, I'm just trying to put my exact thoughts on the screen. Am I leaving something out, or do I have the right idea about this? Thanks a lot guys!

 

[Allday]

hi jones, your reasoning is correct, but you left something very important out of your model ... air.

cheers
-Gabe

 

[jones106]

Thanks allday. So I guess the terminal velocity of the falling bullet (due to air resistance) is less than the initial velocity? I was thinking that its terminal velocity when falling would have to be greater than the initial velocity. So when a bullet is just fired horizontally, does air resistance slow the bullet down progressively to its terminal velocity? (neglecting the fact that gravity would bring it to the ground before it decelerated to its terminal velocity)

 

[ranger]

Here is a discussion from a while back:

No, what you are missing is that everyone else is taking into account air resistance. Without that, there is no "terminal velocity" and a bullet dropped will hit the ground at the same time as a bullet fired on some trajectory. With air resistance, however, that's not true- given enough time to reach terminal velocity, a bullet will, eventually, return to Earth with terminal velocity straight down (since there is no horizontal force, the horizontal component of "terminal velocity" will be 0.
It is true that the fired bullet, in your "airless" scenario will hit with more force since it has a horizontal component of velocity also. But I am mystified as to why you think the mass of the fired bullet will be "considerably greater" than the mass of the same bullet dropped.

Original thread found here:
https://www.physicsforums.com/showthread.php?t=14560