I just wagered $100 against this idea and hope to either find vindication and proof, or to prepare to eat crow and pony up.
My neighbor said that he was sure that if you fire a gun on a straight level and from the same height simultaneously by hand, drop a bullet, the two bullets would always reach the ground at the same time.
That can’t be right, (can it?) but I could not prove it–obviously hard to test experimentally.
I thought I knew enough physics to explain why the equations for those two falling objects would necessarily make that doubtful, momentum or vector, or even escape velocity (help me–I’m an English major), or something, has to make it where the simultaneous landing is not necessary.
We ruled out the curvature and topography of the earth etc, so it’s basically in a vacuum on a plane. (would the plane take off?–hehe) But I guess I need an explanation to prove my case and get my money.
Sorry, you lose.
In your perfect case, the acceleration the the y-axis is exactly equal for both bullets - and that is the acceleration due to gravity.
ugh–I thought that in the equation for two falling objects, a large force on one of them would create some difference–and what if it was shot so forcefully that it never hit ground?
Sorry, nope, that’s one of the insights of physics. Too bad your bet didn’t involve orbit around a black hole or the speed of light. Then you might see a difference. A horizontally launched rocket would also hit the ground at the same time as its twin, unless it was aimed a little upward, which is cheating.
Read Cecil’s article. You’re right, but at the heights/velocities that are reasonable for a hand held gun, it’s an insignificant fact and so your neighbor is also right.
On an infinitely long flat plane in a vacuum, they will fall at the same speed. This is the model your neighbour, undoubtedly, intended.
wait, is it impossible to hit an object one time hard enough for it to reach escape velocity and actually escape or whatever it’s called–just never hit the ground?–(then I’m done looking for a loophole;))
and I’ll go read the article–ya’ll were just very fast in responding -thank you
If a bullet is shot perfectly horizontally, then its initial speed in the vertical direction is zero - same as the one you dropped. The force in the vertical direction on both bullets are the same, i.e. gravity. So they both move in the vertical direction the same way.
I think the counter-intuitive aspect is that the three spatial dimensions are completely independent. The force or speed in the horizontal direction does not affect the motion in the vertical direction. Of course that’s only true if the object doesn’t interact with anything else. If it bounces off a tilted surface, for example, of course the horizontal motion can be converted into vertical motion. Or if you put a wing on the object and let it interact with air, forward motion can be converted into upward force.
Oh, certainly, if you had a big enough gun with a small enough projectile and enough propellant (handgun, probably not). The issue is you ruled out the curvature of the Earth, with a long, infinitely flat plane there IS no escape velocity, leaving you somewhat screwed.
If you’re really, really, really desperate you could try and make a case that the length of the barrel of the gun delays the fired bullet’s descent ever so slightly because something is blocking it from going down for a really small fraction of a second, but that’s what we like to call “grasping at straws.”
Another straw you could grasp is air resistance: because air resistance isn’t linear (unlike gravity), how fast an object is moving sideways does affect how much upwards air resistance there is. Theoretically, the fast-moving bullet should fall slightly slower, if you account for air resistance.
But if I were judging this, I’d tell you to pay the man his money.
One easy way to see this is to realize that the motion of either bullet just depends on the choice of reference frame – i.e. viewed from the bullet you shot, it’s equally valid to say that the other bullet is zipping away at whatever the typical velocity of a bullet is, and its own (horizontal) velocity is zero. It’s called the relativity of motion – you can’t, in an absolute way, determine which of the two is the ‘moving’ bullet, as long as the motion at least along the relevant axis is constant.
Thus, there can’t be any difference between the two.
An infinite flat plane does not have an escape speed in any direction: Anything fired up will eventually come back down, because gravity never dwindles away. And on any object which does have an escape speed, direction is completely irrelevant (assuming no air resistance): Shoot a bullet at escape speed in any direction (including down, if you put a bullet-sized tunnel through the ground in the right place), and it’ll escape.
Someone here can probably scare up a video of the classic device that physics teachers use to illustrate this phenomenon. We used to call it the “shoot the monkey” demonstration. A ball is shot from a springloaded gun. At the same time that it leaves the mouth of the barrel, another ball is dropped, several feet in front of it, from the same height, in a direct line with the projectile. (It’s usually tripped by a break in the electromagnet circuit holding the ball up). What you would see is that the ball that is shot will collide with the ball that is dropped, demostrating that they have both dropped the same distance in the same amount of time, separate and unrelated to the fact that the shot ball is also moving horizontally.