noblepa wrote: ↑Fri Feb 03, 2023 10:08 pm
RTH10260 wrote: ↑Fri Feb 03, 2023 8:50 pm
IFF one shoots up vertically, the bullet ought eventually drop back. Stepping out of the landing zone is advised
If one shoots perfectly vertically, and the bullet travels upward for three seconds and falls back to earth in three seconds, for a total flight time of six seconds, the earth will have rotated 1 2/3 miles under the bullet (assuming earth surface speed of 1,000 mph). Farther if bullet travels for more than six seconds.
The shooter is in no danger.
Someone 1 2/3 miles to the west had better watch out.
ETA: I just did a little google-fu and found that the muzzle velocity of a 30-06 hunting rifle varies between 2,700 and 3,100 feet-per-second, depending on the type and quantity of powder used, weight of the bullet and barrel length. If I remember my high school physics correctly, that means that a 30-06 round fired directly upwards at 2,700 fps, will travel upwards for 21 seconds (total flight time: 42 sec.) and will land 11.6 miles west of the location from which it was fired.
And a 30-06 is not a particularly powerful rifle.
You're forgetting the initial angular velocity of the bullet
Using w for angular velocity (instead of the correct lower case omega), you have w=v/r. We can assume v = 1,000 mph for both the ground and the bullet, but r does change with altitude, so there will be a slight lag. Montana is at about 45 degrees latitude, so we can multiply the radius of the earth (3,960 miles) by inverse of square root of 2 (.71) to get r
0 of 2,800 miles (we need this because the earth is spinning on an axis, the radius of the circular motion is dependent on latitude). According to Mythbusters (which I admit can be dicey at times), a 30-06 would go about 10,000 feet up, but because of drag, it would take about a minute to land. So our r
peak would be 2,801 miles. Let's now look at how much faster the bullet's lateral speed would have to be to land on the same spot - that is, constant w. v
peak = v*r
peak/r
0 = 1,000*2801/2800 = 1,000.36 mph. To be conservative, let's assume the bullet is at the peak altitude the entire minute (obviously it will be less than that). Given our delta v, 0.36 mph, the bullet will lag by less than 0.36 mi/
hr * 1
min *
hr/(60
min) = .006 mi = 34 feet. In reality, it'll be a bit more than half that, maybe 20-25 feet.