### Re: Can a bullet mortally wound when coming down from being fire

Date: Thu Dec 17 12:24:20 1998
Area of science: Physics
ID: 912487958.Ph
Message:
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Hello,

Yes, a bullet could mortally wound for such a case...I'll explain why:

If you were to aim a gun straight up in the air and fire it, the
physics that follows is actually pretty simple.  The bullet leaves the gun
with some initial velocity which is called the muzzle velocity of the
projectile.  This velocity will vary with the caliber and the shells
used.  On average I would say that a good number for a muzzle velocity
would be something on the order of 500 to 900 m/s.  For example, a 30
caliber bullet sizzles along at 900 m/s when leaving the barrel.  Just to
give you an idea of how fast that is, the speed of sound is about 330 m/s,
so the bullet in our example is moving at supersonic speed.
Ok, back to the situation, the bullet leaves the muzzle and travels
straight upward.  Just like any projectile, the bullet slows down as the
pull of gravity causes it to deccelerate.  The bullet reaches its peak
height and stops for an instant.  If we neglect wind and friction of air,
the bullet will start to fall and accelerate towards the earth along the
same path it took to get there.  The bullet will then reach a high
velocity and actually return to its point of origin (the gun or with any
bad luck...the shooter) with the same speed that it left.
On the other hand, if we want to include the consideration of air
friction to make this situation have a realistic outcome we have to
consider such factors as resistive forces such as drag and also to see
whether or not we have to consider something called terminal velocity.
Terminal velocity is the idea that a falling object in a resistive medium
like our atmosphere will reach a peak velocity.  The resistance of the
medium prevents the object from moving any faster and provides an opposing
force to slow the falling object down.
This is something that is considered all the time in skydiving since
skydivers will plummet towards the earth and will reach a maximum
velocity.  Now, terminal velocity here depends on the surface area of the
object which is facing the earth (A), the density of the air(p), the mass
of the object(m), the acceleration due to gravity(g), and a
proportionality constant called the drag coefficient(C).  The terminal
velocity is calculated as follows :

V(term) = (2mg/CpA)^1/2

The coefficient C is 0.5 for a spherical object and the number can go
up to 2 for irregular objects; I have assumed 1 for the bullet.  I have
also assumed a mass of about 20 grams for the bullet.  The area, A, was
calculated to be 4.56x10^-5 m^2 taking into account that the diameter of
the bullet is about 7.62 mm for a 30 caliber shell.  After doing this
calculation with these factors, I determined the terminal velocity to be :

40.79 m/s  or  91.24 mph

So, instead of the bullet returning to the shooter at 900 m/s, the
velocity is significantly less, but still pretty damaging for such a
speed. Of course, it would be fatal if it struck in a vital area of the
body like the head or chest.  I have assumed that since the bullet was
fired upwards, the impact coming back down would most likely be to the
To summarize, the unfortunate result of this story is that the bullet
leaves the muzzle at 900 m/s  travels upwards, stops, and comes back
towards the shooter and impacts at 40.79 m/s.  Definitely a bad thing if
the world when they fire their guns into the air blindly to celebrate ...

Tye Morancy

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