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Re: A Parents' Day gem




Leigh Palmer writes:

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.

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

It's easier said than done!. Here are some problems that you will face
..... some easier to solve than others in the practical world.

1. How do you release a bullet so it starts falling vertically at the
same instant that the second bullet is fired horizontally?

2. It should take only a half second for a bullet in free fall to drop
1.5 meters. In the same time, a fired bullet travelling horizontally will
be about a half mile away. How do you determine which one hits the lake
surface first? Telescopic coincidence timers?

Herb Gottlieb from New York City
(Where a half mile is greater than the distance from Penn Station (34
Street) to Times Square (42 Street)