# Two Bullets Decent towards the earth

## Main Question or Discussion Point

Hi,

Very uneducated in the wonderful world of Phsyics. I'm a psych major so no physics required.

Today I had a conversation with a gentleman that told me that you if you dropped a bullet from your hand straight to the ground at the same time you fired a bullet from a gun at the same height as the starting point of the other bullet you dropped from your non gun toting hand, with the plane of the fired bullet parallel to the ground that both, I repeat BOTH, bullets would hit the ground at the same time.

I told him it was impossible due to resistance and the force of the bullet traveling from the gun that gravity would affect the rate of descent differently plus the actual weight difference of the bullets, assuming of course the bullet dropped from your hand is without casing, which would be the same for the bullet expelled from it's casing after being fired, that the one dropped from your hand would hit long before the one fired from the gun. If for nothing else other then the fact that the fired bullet is traveling such a great distance that it would take longer to hit.

If somebody could enlighten me. I don't doubt that this is physically possible, it's just hard for me to grasp it. I assume it might be possible in a perfect vacum but who has one that big to be able to fire a gun and allow the bullet to hit the ground by itself?

Thanks all. I hope somebody can help me.

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berkeman
Mentor
Thread moved from General Relativity (?) to General Physics. This doesn't look like a homework problem, so I'll leave it here in the general forum.

Welcome to the PF, bheinz24. The thing you are asking about is true, and it is true because the horizontal motion of the bullet is independent of the vertical motion of the bullet.

When you fire a bullet horizontally, it has some initial horizontal velocity, but zero initial vertical velocity. When you drop a bullet from your hand, it has zero initial horizontal and vertical velocites.

The horizontal motion of the fired bullet depends on its initial horizontal velocity and the retarding force of air resistance. But its vertical velocity, as well as the vertical velocity of the dropped bullet, only depend on the attractive force of gravity. Gravity causes both bullets to increase their downward velocity at the same rate (g = 9.8 meters per second squared), and both bullets will hit the ground at the same moment. The fired bullet will be far away, of course, but on level ground, both will hit at the same moment.

Think about this--If you shoot a bullet downward and drop a bullet at the same time, the one you shot will hit first.
If you were to shoot one up and drop one at the same time, the one you drop will hit first.
If you shoot one slightly down (like 1 degree below the horizontal) and drop one, the one you shot will hit first.
If you shoot one slightly up (1 degree above) the one you drop will hit first. See where this is going?

rcgldr
Homework Helper
The bullets would only land at the same time if the earth was flat. The fired bullet takes a sub-orbital path and lands later.

Even with a flat earth, the fired bullet has spin on it, causing it to resist being rotated downwards, so it has more vertical component of drag on it and again, it lands later.

So what you need is a flat earth and a vacuum for both bullets to land at the same time.