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Re: A Parents' Day gem



"That's LUDICROUS!" said the parent. "ANY fool can see that the forward
momentum of the SHOT bullet will make it spend LONGER in the air that the
DROPPED bullet!"
"I can prove it to you mathematically if you wish," replied the teacher,
"but they will, in fact, hit the ground at the same time."
A pause. Then:
"This is witchcraft!" the parent hollered. "WITCHCRAFT!!!" And he
turned
and stormed out of the classroom.


I've done the experiment with a gun--sort of--to convince a companion.
Pellet rifle shot over a calm lake, another pellet dropped vertically. The
splashes were, at least, very close in time. Of course, we had no way to
accurately level the gun; I tried to hold it level but suspect I
unconciously changed the angle until I got good results.

I did mention things like curvature and so on to my friend. He did not
follow all of that but did decide that his original assumption that a large
forward speed would cause a much larger flight-time was not correct.

It seems this is a good example to connect to the real world. Do the
calculation. You'll see there is an easy way to hold the rifle
sufficiently level.

For a bullet fired in a vacuum, so air resistance doesn't matter, one
can easily calculate the accuracy required in holding the rifle level
to achieve an equal time result within ten percent with fired and
dropped bullets. The result is, for a bullet with a muzzle velocity
of the speed of sound* and a height of 1.5 m above the lake level,
the rifle must be held horizontal to better than two milliradians,
and the requirement for accuracy increases with increasing muzzle
velocity. It is certainly possible to hold on target to this accuracy,
even offhand. If one has a lake that is a kilometer or more from bank
to bank then the feat could be accomplished by aiming at the waterline
on the opposite bank, or better still at a point approximately 1.5
meter above it, for any reasonably wide lake (even 100 meters) with
the rifle boresighted.

Don't speculate; calculate! Real numbers may prove enlightening.

Leigh

*This is faster than a .22 LR and slower than a .30'06. There is a
tremendous range in muzzle velocities (my information is very old -
from my childhood) up to 4400 feet per second (Mach 4) in a load
called a .220 Swift. (I see the 7.62 mm M-14 rifle reaches 853 m/s.
The internet is a handy source of data.)