A bullet droppet and a bullet fired

[TSN79]

I was told something I really found hard to believe. Two cases:

A) You drop a guns bullet from a height of let's say 1 meter.

B) You fire the bullet from the gun horizontaly, also 1 meter above ground.

What I'm told is that these two bullets will hit the ground at the same time if dropped/fired simultaneously since gravity starts "working" on them at the same time. It sounds amazing, can it really be??

[Bystander]

Short answer for purposes of learning basic physics, "Yes." Long answer for purposes of detailed discussion of exterior ballistics, "No." "Yes" assumes an infinite flat plane over which the bullet is fired, and that the bullet travels in vacuum (no lift due to the gravitational density gradient when fired through air or some other gaseous medium).

[HallsofIvy]

Assuming, as Bystander said, "vacuum" and so no air resistance ("infinite flat plane" is not as important; the earth is large enough that its curvature within the range of a typical bullet is negligible) then the only force acting on a bullet is gravity. Downward acceleration is the same in both cases. Since horizontal and vertical motions are independent the fired bullet, which has only horizontal initial velocity, and the dropped bullet have the same initial vertical velocity, 0, and so exactly the same vertical motion.

[TSN79]

Thx, guys :) Still, pretty amazing.

[Bystander]

Earth's curvature? ~4" a mile. Time? 1/4 s to .7s for 2 to 8' drops. Muzzle velocity? 2000-4000 f/s. 1-2" extra drop time? 1-2 or 3% --- actually, for a classic, this is one of the lousier exercises.