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Horizontal Projectile Motion is a special case of projectile motion, in which a projectile is thrown horizontally resulting in a curved trajectory due to the gravity acting on the projectile.

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It can be analysed into two separate motions, a uniform linear motion on the x-axis and a free fall on the y-axis.

OX-axis: The motion is uniform linear with velocity Vx.The equations that describe its movement on the direction (x):

         $ x = V_{x}t $

OY-axis: The projectile does a free fall.The equations that describe its movement on the direction (y):

         $ V_{y} = g t $
         $ y = 1/2 g t^{2} $

At every moment the projectile's speed is: $ \vec{v} = \vec{v_{x}} + \vec{v_{y}} $

The displacement of the projectile: $ d = \sqrt{x^2 + y^2} $

We can assume that the motions happen independently, either simultaneously or successively, with each motion lasting for:

$ t = \sqrt{\frac{2h}{g}} $