The muzzle velocity of a bullet is 1000m per sec. If fired skywards what danger does it represent?

Question

Conventional Newtonian calculations show that it will go up about 1000 metres before the velocity becomes zero and it starts to fall and that the time, before reaching the ground again, is around 3 secs. Such calculations ignore air resistance.

I have been in Greece when enthusiastic football fans have taken to the streets and emptied various firearms into the sky. I assume that air resistance will result in some limit to the missile velocity on return but surely not enough to make the thing safe?

Answer 1

You should have watched "The Mythbusters" on the discovery channell this afternoon! They investigated this!
They spoke to a doctor in the US who documented two cases of injury and death because of reckless use of firearms in the US.
One 4 of july evening in San Fransisco, a man sat on a chair on his balcony, enjoying a fire works display, when he felt a sudden stinging sensation on his thigh. A bullet had struck it at great speed. Someone had foolishly fired a gun into the air and it returned to the ground hitting the unfortunate fire works fan.
On another occasion, a man was talking to his wife outside his house when he suddenly doubled over in pain and collapsed. His wife, fearing he had a stroke, rang for an ambulance and he was rushed to hospital. When they x rayed him they found a bullet lodged in his brain, fired by a similar idiot.
This unfortunate man died and these are the only cases, in the US at least, where it has happened. A ballistics match was run on the bullets and in one of these cases a guy was tried and convicted of the offense.
The bottom line from the mythbusters themselves is don't try this at home. If a returning bullet reaches its terminal velocity, get to some protective cover. The unfortunate man who died above, was talking to his wife under a sheet of corrugated plastic and it didn't do him much good.

Answer 2

First if we consider a bullet fired straight up - eventually it will come to a stop and start to fall back to earth, its maximum speed is then governed solely by its terminal velocity (independent of how fast it left the muzzle). The terminal velocity is the balance between force of gravity and air resistance (air resistance is a function of speed). Since a bullet is relatively light, its terminal velocity will be no where close to the muzzle velocity. (Mythbusters did an experiment dropping a penny off a highrise, and found it poses no danger).

Yet, there are many reported cases of injuries caused by careless use of firearms. I would suggest these are likely caused by not firing straight up. If a gun is fired lets say above the heads of a crowd - That may only be 20 degrees inclination, now the bullet will come back down but will not have lost all of its horizontal velocity yet. So it could come down a few blocks away and seriously injure / kill.

Answer 3

Once the bullet hits it's apex it will begin to free fall at 9.8 ft./sec squared. It will reach it's terminal velocity which is not the same as it's muzzle velocity on it's way up. Terminal velocity will be determined by the shape of the bullet (air resistance). Most likely not enough to kill you, but would certainly hurt like hell. Example humans free falling reach a terminal velocity of approx. 125-150mph.
The theory that a penny dropped from the tallest building could kill you is false. It doesn't have the mass required to break the surface of the skin. The show Mythbusters proved that even a penny shot at a higher velocity than it's terminal velocity couldn't break the skin of a human (experiment done with a human volunteer)

Answer 4

This applies only if the bullet is fired perfectly vertically. If there is just a small departure from the vertical, the bullet will travel in a ballistic trajectory, point first, and will come down at almost the same speed as it went up, with lethal capability. The Mythbusters tried it (episode 50), and uncovered some actual cases where people died as the result of someone carelessly firing a gun up in the air, as far as one kilometre down range.

You may want to check you calculations, however. A bullet with 1000 m/s muzzle velocity will take 102 seconds to slow down to zero if we neglet air resistance. That would take it several dozen kilometers high.

Answer 5

No, i do not imagine air resistance will be an major ingredient pondering the type of the bullet. At 80 (is that 800?) ft/s, it gained't make contributions a lot. From the kinematic equation for consistent acceleration it is used at the same time as time isn't given: y_f = y_i + (v_f^2 - v_i^2)/2a the right reached is given by using y_f - y_i = h = (v_f^2 - v_i^2)/2a because you're searching for for for correct, the really values of y_f and y_h are beside the point to you. what's major is the adaptation of both, so that you do not want to worry about that. Set v_f = 0, because the bullet stops at optimal correct. v_i is 80 ft/s. a = g = 32 ft/s^s. you could remedy for h. Then, once you've solved for h, you should use both of both very last kinematic equations for consistent acceleration: v_f = v_i + at or x_f = x_i + v_it + (a million/2)at^2 to remedy for t. personally, I want the former because the 2d equation can furnish a 2d order polynomial with appreciate to t.

Answer 6

If fired straight up. It will go until it runs out of power and then fall by the force of gravity. Since the bullet has little mass, gravity cannot make it go quick enough to do serious damage. However, if the bullet is fired at an angle, it is possible for the bullet to still have significant velocity when it hits something. This is what is truly dangerous. Firing straight up isn't a big deal. Firing at an angle is.

Answer 7

Let θ be the angle to the horizontal at which the bullet is fired. Then
Vy = Vsinθ
Vx = Vcosθ
1,000 m/s is a pretty high muzzle velocity. 400 m/s is more realistic.
h =((Vsinθ)^2 - 0)/(2g)
T1 = (Vsinθ)/g = T2
R = (T1 + T2)Vcosθ
R = 2V^2sinθcosθ/(2g)
R = V^2sinθcosθ/g
Rmax occurs @ θ = 45°
Rmax = V^2/(2g) = 1,000,000/(2*9.80662) =
A = πR^2
A = πV^4/4g^2
Below is a table of max range and area of mortal danger versus muzzle velocity.
V (m/s)range (km) Area (km^2)
100..... ..... ..... 0.5 ..... ..... . 0.8
200..... ..... ..... 2.0 ..... ..... 13.1
300..... ..... ..... 4.6...... ..... 66.2
400..... ..... ..... 8.2..... ..... 209.1
500..... ..... ... 12.7..... ..... 510.4
1000..... ..... .. 51.0..... ... 8,166.8

I suggested 400 m/s because that yields a range comparable to that published by Winchester for the .30-06 bullet (5 mi)

It can be argued that the probability of hitting someone with a random shot is very small. The counter argument is that you can't know where the bullet will strike. A person totally unaware of distant events can be killed or maimed with no warning whatsoever.

Answer 8

Disregarding air resistance, an object will come down with the same velocity it goes up at. So even with a lot of velocity lost to air resistance, a bullet fired in the air can do some damage.

Answer 9

I work in Chicago in the industrial sector and have been on top of a lot of big buildings and factories. There are always a few bullets found from when people fire off a few rounds into the air. One engineer I know has a beer stein full of bullets he has collected over the years.

Answer 10

if fired directly above head then it will get to a point and fall directly back down gathering speed all the time danger being it could kill sum1 this of course depends on whether there is any greater wind speed the higher up in the sky it is.if fired at even the slightest angle then it will travel in an arch and could kill sum1 bout 4 streets over if it doesnt hit anything first.