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Old February 4, 2008, 07:47 PM   #45
warrior poet
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Join Date: December 13, 2007
Location: Whereever Uncle Sam wants to put me
Posts: 415
Oy vay. Calculus... again... Okay. You asked for it. For something fired straight up, the bullet slows according to: Distance = initial (muzzle) velocity * time - 9.8 meters per second PER second * time. (This is the simplest one, not including wind resistance.) To include that.... You would also subtract the Area under the curve defined by the integral for the force of friction with respect to instantenous velocity. Leaving a system of equations with respect to three related variables- time, coefficient of friction and velocity.
YUCK! All of that will yield the max height of the bullet, which gives the gravitational potential energy. From that you again subtract the wind resistance, giving the kinetic energy on impact with the Earth.
All of this is moot, because it is IMPOSSIBLE to predict the bullet's coefficient of friction on the return trip b/c it is no longer stabilized by its spin. Net result... a statistical window in which three standard deviations will fall- roughly 99% of all bullets fired thusly. Would it kill when it hits... statistically no, but that only accounts for 99%.... there is always that slim chance that it might self-stabilize on the return trip, and be lethal. That is the mathematical answer... period. It isn't a physics problem, but one of statistics, b/c there is NO definitive way to predict wind resistance on the return trip. Okay?
Now, I'm going to enjoy some scotch... and kill off those offending brain cells I just used.
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