While real bullets tumble and are a more complex shape, I just ran a
spreadsheet simulation using a 10 gram, 0.6cm spherical bullet. At initial
velocities of 1000 m/s (but with the same results at 500 m/s) I'm getting
the same final velocity of the bullet fired anywhere from 5 degrees to 90
degrees (within a very small range). Namely, about 50 m/s. I used a time
increment of .01 seconds, a damping factor b = .5xCxrhoxA with C = .5 and
an overall b of .0000387. I let g stay constant at 9.81 and assumed a
v-squared dependency. The flight times ranges from 12 to 27 seconds for the
1000 m/s initial velocity. If you want to try this, the only complication
is that the air-resistance induced acceleration changes sign after the
bullet starts down. I just adjusted that manually with each trial (changing
angle).
I think this might suggest that once the bullet starts tumbling (if it does)
then the final velocity really doesn't depend on the angle fired. Can
anybody confirm or refute these calculations?
Rick
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Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN
rtarara@saintmarys.edu
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Free Physics Software
PC & Mac
www.saintmarys.edu/~rtarara/software.html
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