The Physics of Projectile Motion
Here are some formulas that describe projectile motion: 
Once the object leaves the table, it experiences a downward acceleration equal to gravity (9.8 m/s/s). Thus the vertical velocity (Vy) is continually increasing. The horizontal velocity (Vx) remains constant and is equal to Vxo. The two vectors Vx and Vy are added together to get the velocity at each point on the path. 
If an object is pointed at an angle, the motion is essentially the same except that there is now an initial vertical velocity (Vyo). Because of the downward acceleration of gravity, Vy continually decreases until it reaches its highest point, at which it begins to fall downward. 
History
This illustration reflects the general opinion of projectile motion before Galileo. The theory was based on Aristotle's views of motion and held that a shot object (a cannon ball, for example) followed a straight line until it "lost its impetus," at which point it fell abruptly to the ground. 
Later, Galileo realized that projectiles actually follow a curved path, as this following illustration shows. Galileo said that projectile motion could be understood by analyzing the horizontal and vertical components separately. The drawing is by Niccolo Tartaglia. 

Galileo understood that the projectile's path is a combination
of horizontal and vertical motion.


Galileo understood that
vertical motion does not affect horizontal motion. An object projected horizontally will reach the ground in the same time as an object dropped vertically. No matter how large the horizontal velocity is, the downward acceleration is always the same. 

Gravity accelerates an object downward even if it is moving horizontally. 
Galileo was able to show that a projectile is controlled by two
independent motions, which work together to create a precise mathematical
curve. He actually found that the curve has an exact mathematical shape, a
shape that the Greeks had already studied and called the parabola. The
path of any projectile is a parabola.