If the Earth were a perfect sphere with no atmosphere (only gravitational forces) and you are at the equator and facing directly spinward (i.e. toward the direction of rotation), and you fired a bullet directly upward, where would it land in relation to you? In front of you, behind you, or on your head?
For those of you who would actually like to do some math: If the bullet had a muzzle velocity of 500m/s, and the Earth has a rotational velocity of 465m/s at the equator, a uniform gravitational acceleration of 9.8m/s at all altitudes (for simplicity's sake), and a circumference of 40,000,000 meters... calculate the distance from you that it would land.
2006-06-16 08:06:33 · 11 answers · asked by stellarfirefly 3 in Science & Mathematics ➔ Mathematics
Give it a little bit more thought, guys and gals. The Earth is not a flat plane moving in the direction of your facing. It is a rotating sphere. ^.^
2006-06-16 08:16:44 · update #1
Yes, of course, gravitational acceleration is 9.8m/s^2, not 9.8m/s. Stop nit-picking and solve the problem already. -.^
2006-06-16 09:18:19 · update #2
A few more items for the nit-pickers: Don't worry about calculating its trajectory while still inside the barrel; if it pleases you, assume there is no barrel, or assume that the tip of the barrel is the (0,0) origin so that "on your head" really means "back at the tip of the barrel". And yes, assume the bullet is a point, the origin is a point, etc. so that even a 0.01m variation would be either "in front" or "behind". And the absense of atmosphere means no terminal velocity.
So again, stop nit-picking and answer the question. ^.^ Would it fall in front, behind, or return to its origin? And most importantly, why?
(Lastly, the math portion is *not* trivial, despite the apparent simplicity of the problem. Extra points to whomever can explain or give examples as to why this is.)
2006-06-16 09:27:16 · update #3
I think it would land behind you because as it rises, the rotational speed of the bullet around the earth would have to increase in order to keep up with you because it's going around a larger circle. Of course, if you're going around a sphere, that could also be considered to be in front of you. Also, I doubt that the bullet would fall at the same speed that it was shot. I don't think that gravity would get it going as fast as the gun did.
2006-06-16 08:33:12 · answer #1 · answered by Brent 2 · 2⤊ 0⤋
Excusing the confusion: Save your head as it will fall directly on your head.
Reason: The rotational velocity will be same for you as well as the stone. Has there been atmosphere then the rotational velocity of stone would have decreased because of resistance and the stone will fall behind you.
2006-06-16 15:17:30 · answer #2 · answered by muks320 3 · 0⤊ 0⤋
On your head. The velocity of the earth is added to the velocity of the bullet as a vector. That vector would, in your senario, bring it specifically right back down the chamber of the gun about 19 seconds later.
2006-06-16 15:13:26 · answer #3 · answered by wizard8100@sbcglobal.net 5 · 0⤊ 0⤋
due to the muzzle of the gun rotating radially equally with the rotation of the earth the bullet would theoretical land right back in the muzzle. not only that but with no atmosphere to create drag, it would be traveling at the same velocity when it comes back down as when it was fired due to gravity is the only thing slowing it down as it is going up and the same gravity will equally propel it back down.
2006-06-16 15:22:05 · answer #4 · answered by sprcpt 6 · 0⤊ 0⤋
It would land behind you. When the bullet loses contact with the surface, it carries the same rotational velocity as the surface. But it needs more rotational velocity at the top of its flight to keep up with you. Hence it can't keep up, and drops behind you.
2006-06-16 15:46:51 · answer #5 · answered by Keith P 7 · 0⤊ 0⤋
It will fall on your head but its ok, it will not kill you. The popular show "Mythbusters" did the expirement and easily showed that the terminal velocity of the bullet tumbling back to earth was not enough to even pierce the skin of the body. They checked this directly using pig's heads and the ever favorite balistics gel.
2006-06-16 15:42:46 · answer #6 · answered by Blame Canada 1 · 0⤊ 0⤋
I am not a great physics person but here goes:
Because the bullet is technically moving at the same speed as you are originally, it will land directly on top of where you fired.
Just a guess though.
2006-06-16 15:10:28 · answer #7 · answered by cosmo5847060 3 · 0⤊ 0⤋
It would come back down into your head, depending on the curve and wind.
2006-06-16 15:09:50 · answer #8 · answered by Jake H 3 · 0⤊ 0⤋
If there is no atm than there is no "you".If there is no " u "than there is no gun .If there is no gun than there is obviously no bullet!
and last but not least If there is no u than there is no head of urs!
so ........and dear sir acceleration is not 9.8 m/s it should be 9.8 m/s^2
2006-06-16 15:31:41 · answer #9 · answered by face of death 1 · 0⤊ 0⤋
on your head I agree with cosmo, It would probably kill you too since it will land with nearly the same speed as it left with
2006-06-16 15:11:42 · answer #10 · answered by dhaval70 2 · 0⤊ 0⤋