|MadSci Network: Physics|
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 head... 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 you ask me. Just think about this when you see those festive celebrations around the world when they fire their guns into the air blindly to celebrate ... Tye Morancy
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