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If you drop a 45 caliber bullet from 5' and simultaneously shoot a 45 caliber bullet straight ahead which bullet will hit the ground first?

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Simplistically, the downward acceleration will be the same. But, the shape presented to vertical motion by the bullets is different. One is on its side, the other one points down. Also, one is moving very quickly and has a disturbed airflow around it, which will affect its vertical drag.

So - I would not like to predict which would hit the ground first - too many unknowns.

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Say you're in a vacuum and both projectiles are pointed in the same direction.
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In a vacuum I would think the dropped bullet would hit first. Also it could make a huge difference with the projectile. Full metal jacket would have a longer flight than a lead hollow point. Too many unknowns but would love to send mythbusters on it. How you waldorf
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Hi Richard, I'm just fine, thanks. How you?

There's another issue. The bullets hit the ground a long way apart. What are the chances of the ground being level? None at all, I would say.

Too many unknowns....
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You need to come out it a equation for that. Take measurements @ barrel, 50ft, 100ft... Figure out time of flight between stations as it slows down. Speed+ time= drop...? Then starting at a hight of 5ft do the math until your at 0'0"... Right?
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The horizontal flight has absolutely no effect on how fast the bullet falls. Gravity doesn't care how fast an object is moving horizontally. You are adding all sorts of conditions that have no relevance to the equation. To adjust for air resistance, just drop the stationary bullet in a horizontal attitude, don't point it down.
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at the same time if they are from the same heighth and you shoot straight

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The learned this in my sheriff's academy.....the same time

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Really?
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Gravity is always the same. As long as the bullet is shot horizontally and not upward or downward, both will hit the ground at the same time. Obviously, the shot bullet will be hundreds of feet away, but horizontal velocity has no effect on the vertical velocity caused by gravity.

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this would be correct if both objects have same power behind them.
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What if the bullet was shot into a tornado 500 yards away. Would they still land at the same time?
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What if you dropped the bullet into a tornado? Once you change the conditions the answer changes.
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It's simple the one that will go thru your leg

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Everything, no mater how big will fall at the same speed.

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Neglecting the effects of air resistance, which you rarely can.
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Air resistance doesn't change for the falling objects, they're both bullets and so will have the same change in velocity due to air resistance. Again, the horizontal velocity has no effect on gravity.
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wouldn't the bullet's spinning give it a marginal amount of upwards thrust?

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No but it gives the trajectory of the bullet a slight horizontal drift.
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The shot bullet will hit the ground first because it is propelled from the weapon. Plus at 5' maximum velocity will not be reached

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Nice question. Gravity is the same but it would all come down to time of flight.