Explain the relationship between the horizontal velocity and the ...

[coco]

Explain the relationship between the horizontal velocity and the vertical velocity of a projectile fired into the air from a location on Earth's surface.

[Hungry!]

in terms of a firearm, the horizontal velocity is measured by how far the projectile is able to go distance wise, the vertical velocity has to do with the relationship of gravity and windage in how fast the bullet will be pulled to the earth

[j_sun]

There's no relationship - they are independent.

The vertical will be affected by gravity and wind resistance, the horizontal only by wind resistance.

[Melanie]

The horizontal velocity remains constant.
The vertical velocity keeps changing because of gravity

[Hawke]

You don't give an angle to  horizontal. If it is fired straight up it will lose velocity at the same rate it would gain velocity in free fall, neglecting air resistance. If it is fired horizontally it will hit the ground at the same time as a bullet dropped from the muzzle. Gravity had no effect on forward motion.