Acceleration of a falling bullet
Acceleration is of course not expressed in units of feet per second. The unit of feet per second expresses a measure of velocity, not acceleration. Acceleration is expressed in units of feet per second per second, or feet per second squared. The acceleration of a dropped object due to gravity alone, once again ignoring extraneous, but real, factors such as friction, is 32 feet per second per second, close enough for government work.
This does not mean that our bullet dropped in a vacuum will fall 32 feet every second for however many seconds it is falling. It means that its velocity will increase by 32 feet per second for however many seconds it is falling. As it falls down through our vacuum its velocity gets faster and faster the farther it falls, increasing at the rate of 32 feet per second each second it is falling.
Of course the same thing applies to the downward vector of the velocity of a projectile fired from a weapon, be it the 230 grain FMJ from my beloved M1911 or the 1500 pound armor piercing projectiles from the 14 inch guns on the USS TEXAS, parked just down the road a bit from where I sit -- the same vintage as my never-let-me-down M1911 -- both veterans of WWI. (To hopefully avoid at least one element of incoming, remember that friction and other forces at work are ignored).
Looking at our train again, having a downward velocity of nil feet per second at the moment the rifle is fired, if our bullet hits the ground one second later, accelerating at the rate of 32 ft./sec./sec., the rifle would have been about 16.4 feet above the ground, not 32 feet, again, close enough for government work. The downward vector of its velocity at the moment it strikes the ground would be 32 feet per second. I reckon 16.4 feet is still a rather high elevation for our shooter on the train. Perhaps he was in the cupola of the caboose.
Should someone be tempted to ask, "what does all this have to do with shooting?", I would respond that it has a great deal to do with shooting -- it determines whether you will hit what you are aiming at. This is the basis of the science of ballistics and those trajectory tables most of us have used, particularly the long gunners in the crowd. Of course precision requires cranking in factors ignored in the above examples such as friction, bullet shape, rotation, location on the earth's surface, the motion of the earth, and such, but it all starts with 32 ft./sec./sec.
Of course in the example I recited just to demonstrate a principal, 3 seconds was just picked at random, and the height of the rifle above the ground under the train was intentionally not specified, as I saw nothing to be gained by going into the higher mathematics of the situation and I would have had to dust off the old sliderule. In fact, if it took our bullet the 3 seconds in my example to reach the ground then the rifle would have been very nearly 150 feet off the ground. A big train.
Acceleration is of course not expressed in units of feet per second. The unit of feet per second expresses a measure of velocity, not acceleration. Acceleration is expressed in units of feet per second per second, or feet per second squared. The acceleration of a dropped object due to gravity alone, once again ignoring extraneous, but real, factors such as friction, is 32 feet per second per second, close enough for government work.
This does not mean that our bullet dropped in a vacuum will fall 32 feet every second for however many seconds it is falling. It means that its velocity will increase by 32 feet per second for however many seconds it is falling. As it falls down through our vacuum its velocity gets faster and faster the farther it falls, increasing at the rate of 32 feet per second each second it is falling.
Of course the same thing applies to the downward vector of the velocity of a projectile fired from a weapon, be it the 230 grain FMJ from my beloved M1911 or the 1500 pound armor piercing projectiles from the 14 inch guns on the USS TEXAS, parked just down the road a bit from where I sit -- the same vintage as my never-let-me-down M1911 -- both veterans of WWI. (To hopefully avoid at least one element of incoming, remember that friction and other forces at work are ignored).
Looking at our train again, having a downward velocity of nil feet per second at the moment the rifle is fired, if our bullet hits the ground one second later, accelerating at the rate of 32 ft./sec./sec., the rifle would have been about 16.4 feet above the ground, not 32 feet, again, close enough for government work. The downward vector of its velocity at the moment it strikes the ground would be 32 feet per second. I reckon 16.4 feet is still a rather high elevation for our shooter on the train. Perhaps he was in the cupola of the caboose.
Should someone be tempted to ask, "what does all this have to do with shooting?", I would respond that it has a great deal to do with shooting -- it determines whether you will hit what you are aiming at. This is the basis of the science of ballistics and those trajectory tables most of us have used, particularly the long gunners in the crowd. Of course precision requires cranking in factors ignored in the above examples such as friction, bullet shape, rotation, location on the earth's surface, the motion of the earth, and such, but it all starts with 32 ft./sec./sec.
