About a year ago there was a thread on how far a bullet would travel.
Someone, Mike Graham IIRC, posted the balistics for a 22 long rifle
bullet. Since I still had that data on file, I ran it through my
balistics program for a near vertical shot. Here are the results:
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Given the velocity of a 22lr bullet at the muzzle and 100 yards as
1280 1017 fps respectively, I convert to metric and get
390.14m/s and 309.98m/s at muzzle and 91.44m. From these values, I
calculate the drag coefficient, km (dV/V per meter), of .002515.

Using this result and the muzzzle velocity, V0, I can calculate the
point, x1, at which the upward velocity is 0 and the point, x2, at
which the bullet has returned to the level of the muzzle. Thus,
assuming an 85 degree angle of elevation,
x1= 86.4
x2= 133.7

The positions, velocities and times at the muzzle, x1 and x2 are then

Show_flight V0 km 85 Bflight 0 x1 x2
x y Vx Vy t

0 0 34 389 0
86 729 5 0 9
134 0 1 ²61 25

Summarizing, the bullet reaches a maximum height of ~730meters where
its horizontal velocity has dropped from 34m/s to only 5m/s. Back
at the initial height, the horizontal velocity is now 1m/s, it took
almost twice as long to come down as it did to go up and its velocity
is less than 1/6 of its muzzle velocity.

Due to the complexity of the math in getting these results, the high
school physics approach to this problem ignores air friction,
i.e. sets km=0. If we do this, we get

x1= 1348.5
x2= 2697.1

Show_flight V0 0 85 Bflight 0 x1 x2
x y Vx Vy t

0 0 34 389 0
1349 7707 34 0 40
2697 0 34 ²389 79

Note that this simplified approach gives a maximum altitude over ten
times too high. Also note that without air resistance, the horizontal
velocity would remain constant, the bullet would take the same time to
come down as to go up and would be travelling at its muzzle velocity
when it got back down.

Although the "no air resistance" approach is a good introduction to
some of the concepts involved, it is not adequate to solve balistics
problems in the "real world".
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If anyone wants the details of the calculations and can read APL, I'd be
happy to send them to you.

Ted