[Edwin Brennan]

Edwin Brennan  asked the Naked Scientists:

My scientific friends assure me that a bullet fired from a rifle held horizontally will hit the ground at exactly the same time as a bullet from a rifle held vertically, pointing downwards. Fair enough, being a linguist, I was rotten at science, but their explanations seemed to defy common sense. Can you explain it to me, in words of one syllable?
Many thanks,

e.c.brennan

What do you think?

[DoctorBeaver]

That cannot be true. Think about it. The muzzle velocity will be the same regardless of the angle the gun is fired at. Therefore, the bullet will travel the same distance in the same amount of time regardless of the angle. If you point the rifle down & fire, then the bullet will only have to travel a couple of feet before it hits the ground. If you hold the rifle horizontally & fire then in the time it took the bullet to hit the ground when fired downwards, the bullet will travel the same distance forwards in that period of time; a couple of feet.

[LeeE]

A bullet fired horizontally should, in theory, hit the ground at (roughly) the same time as one dropped vertically.  Both start with a zero vertical vector and are subject to the same force of gravity (the vertical vector) but the one fired horizontally is moving much faster through the air and will be subject to aerodynamic effects.

If the fired bullet tilts towards the ground as it drops due to gravity it would have a negative Angle of Attack through the air, producing negative lift, and may actually hit the ground first.  If, on the other hand, the bullet just sinks but remains horizontal, it will effectively have positive AoA, which will give it some lift and extend it's flight.  If it starts tumbling anything could happen.

[lyner]

Edwin.
Were you told this in a Pub, by any chance?
What you heard was a garbled version of the true story.
It could have been his memory, his slurred speech or your slurred hearing or, perhaps, all five. If he was 'really Scientific' he'd have known the proper answer.

For a flat Earth with no atmosphere, a bullet fired horizontally will  take the same time to hit the ground as one which is dropped. Their horizontal and vertical motions are independent.
For a spherical Earth with no atmosphere, if it's fired fast enough, horizontally, it might never hit the Earth - it would be in a just above ground orbit.
For 'real' speeds, the curvature of the Earth would still delay the impact of the 'fired' bullet a bit, because it would have to fall a bit further.
In real life, the aerodynamics of the bullet make it harder to predict and LeeE's comment could well apply.

I think the 'required' answer is that they hit at the same time.

[DoctorBeaver]

I think the 'required' answer is that they hit at the same time.

If the bullet were dropped, that may be true. But check the question.

Then again, it depends how high above the ground the rifle is when fired vertically downwards.

[lyner]

Of course I read the question but it clearly can't be the right one.
Well, you know what I mean - with respect and all that.
The obvious answer to the question, as stated, just follows common sense. There is no paradox or misdirection in the question. Who could be surprised at the answer?

The question, in its amended form, is used to demonstrate the independence of motions in quadrature and the general way that vectors work.

It's a classic.

I reckon.


btw, why would the height matter (on a flat earth)?

[DoctorBeaver]

btw, why would the height matter (on a flat earth)?

It doesn't matter if the Earth is flat, round or shaped like a 1-legged teddy bear; the further above the ground you are, the longer the bullet will take to hit it when fired vertically downwards.

[LeeE]

Actually, after thinking about it again, you'd only get +ve or -ve lift if the axis of the bullet differs from it's trajectory, assuming that air it passes through is stationary.

So if the bullet stayed horizontal while it dropped, it should gain lift, but the axis would have to dip below it's trajectory for it to have -ve lift.

I think...  []

[lyner]

btw, why would the height matter (on a flat earth)?

It doesn't matter if the Earth is flat, round or shaped like a 1-legged teddy bear; the further above the ground you are, the longer the bullet will take to hit it when fired vertically downwards.

Yebbut it would still get there sooner than the horizontally fired bullet (unless you shot the teddy bear through the foot) if it was fired downwards. It wasn't a quantitative question.
I still hold that the original question / statement was not what the original originator meant.
Perhaps Edwin Brennan could go and ask what the original original question was and carry some of our feedback back to the source.