Can Mythbusters explain this?

Question

I'm asking this because of the previous question about shooting bullets in the air. (2nd to last paragraph)

http://www.azcentral.com/news/articles/0702gl-gunfire0702-ON.html

There's a law against firing guns in the air. It's called Shannons Law.

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Oh, and it's a felony.
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Answer 1

Good for you...you did some original research and uncovered the facts. People get killed by stray bullets fired into the air. Shannon was one of them.

Let's look at the physics...since you posted this in a physics section.

When fired straight up out of a gun of any kind, the bullet has kinetic energy KE = 1/2 mv^2; where m is the mass of the bullet and v is the muzzle velocity of that bullet. From the time the bullet leaves the muzzle, gravity (G) is tugging on the bullet to slow it down. Also, as long as the bullet is moving through air, there is also a drag force D = 1/2 rho Cd A v^2, like a friction force, pulling downward to slow the bullet.

But bullets are designed to knife through air, which is why Cd, the coefficient of drag, and A, the cross sectional area, are very small. Thus, D is very small compared to G and F, the force of the explosion that gave the bullet its muzzle velocity. Thus, we can discount D, both going up and coming back down.

Eventually, at some height h, the bullet will stop and all its kinetic energy going straight up at the muzzle will have been converted to potential energy PE = Gh = mgh; where g = the acceleration due to gravity (e.g., 9.81 m/sec^2) and h is the height above ground where the bullet finally grinds to a halt because of gravity.

Now here's where the laws of physics come into play...energy is neither created nor destroyed, but it can be converted. This is called the law of conservation of energy.

In this shooting in the air case, the KE is converted into PE as the bullet travels upward. And (this is important), the PE is converted back into KE when the bullet falls back to Earth. In fact (this is VERY important), all the PE becomes KE on impact with the point from which the bullet was fired.

In math talk, we have KE(up) = PE = KE(down); so that 1/2 mv(up)^2 = 1/2 mv(down)^2 giving us v(up) = v(down). And there you have it, the velocity of the falling bullet v(down) just before it hit Shannon on the head was the same as v(up)...the muzzle velocity of that bullet as it left the gun. And, I think anyone will agree, bullets coming out of the muzzle of a gun are deadly.

The only reason more people don't get killed by those crazies who fire into the air is because there is a heck of a lot more empty area than there is area occupied by people. The bullets come down and have more empty area to strike than people area; and that's the only reason more people don't get killed.

Again, good for you doing research. And now you have the physics (the conservation of energy) for why bullets coming out of the sky can be as deadly as bullets coming out of the muzzle of a gun.

Answer 2

The Mythbusters test was on a bullet shot STRAIGHT up in the air, so 90 degrees perpendicular to the ground. Fired straight up, a bullet will not obtain a ballistic trajectory and velocity.

A bullet fired at any other angle will obtain a ballistic trajectory which will fall much faster and is capable of killing people, and does.

They did mention this in the mythbusters episode by the fact that they gave it all 3 ratings, busted for the firing straight up part, plausible at other trajectories, and confirmed by eyewitnesses...

Answer 3

At the top of it's trajectory, the bullet will most likely, due to it's aerodynamic shape, turn over and come down nose first.
By the time it reaches ground level again it will probably be at, or near, to its terminal velocity and, even an object so small, will have the force and ability to kill or at least seriously injure.
I don't think a degree is needed for that.

Answer 4

Myth-busters got it right. What makes one think that the bullet turns around when it comes to it's apex? It will tumble back to earth and air resistance has a definite slowing effect on it.