Theory of Gravity Question

[OpenIntro]

We have a debate going on here, and I am not fresh enough on my physics in order to explain the reason why I am right.....I think....lol....

It's a question of gravity....

I know that if two objects are DROPPED at the same height, they will hit the ground at the same time. That's a given. The argument is, if an object is dropped from height x....and an object is, for argument's sake, shot from a gun....will they hit the ground at the same time? One has velocity, and the other doesn't. Does this make a difference?

If someone could explain this out with formulas, it would be much appreciated!

[Tide]

They will reach the ground at the same time only if the one shot from a gun is fired horizontally in a UNIFORM gravitational field and in a vacuum! Since the Earth is round the gravitational field is not uniform and we have an atmosphere so the landing time will generally be different. Of course you may adjust the angle of the projectile (very slightly!) to force them to land at the same time.

In a uniform gravitational field and in a vacuum they will reach the ground at the same time when the bullet is fired horizontally because the horizontal and vertical motions of the projectiles are independent of each other.

[jcsd]

Assuming all else is equal and neglecting the effects of air resitsnace, etc. (which shouldn't quakitvely effect the results): it depends on direction that the object is shot : if it is shot towards the ground (i.e. the compnoent of it's velocity downwards is postive) then it will indeed it the ground first. If it is shot parallel to the ground then the two objects will hit the ground at the same time and if it is shot away from the ground (i.e. the component of it's velocity downwards is negative) then it will hit the ground after the object that is simply dropped.

This si as the initial velocity downwards will help to determine the average velocity downwards.