Projectiles and effects on gravity

[kylera]

Neglecting air resistance on Earth and regardless of how fast or slow a projectile's initial horizontal velocity is when fired from the same fixed height, they will all fall at the same time. Is this because regardless of the horizontal motions, the vertical motion is the same? Can someone clear this up in more layman-like terms? Much thanks in advance.

 

[Hootenanny]

Neglecting air resistance on Earth and regardless of how fast or slow a projectile's initial horizontal velocity is when fired from the same fixed height, they will all fall at the same time. Is this because regardless of the horizontal motions, the vertical motion is the same? Can someone clear this up in more layman-like terms? Much thanks in advance.

This statement is equivalent to saying that neglecting air-resistance, everything accelerates towards the Earth at the same rate. So if you drop any number of objects from a given height, they will all hit the floor at the same time. In other-words, they will all spend the same amount of time in the air (flight time). Now, if you project an object horizontally it will have some horizontal velocity, but that doesn't matter since it is still accelerating towards the Earth at the same rate as if it was dropped. Therefore, the flight time will still be the same as if it were dropped.

Does that help?

 

[kylera]

Yes, that does clear some things up. Much thanks.

 

[mathman]

There could be some variation due to the curvature of the earth. If a projectile starts out horizontally and very fast, its distance to the ground will be larger than for a slow projectile.