Horizontal projection

A body projected horizontally moves under gravity: horizontal velocity stays constant while the vertical motion is free fall — treat the two directions independently with suvat.

Mechanics · Projectiles

Horizontal projection

A body projected horizontally moves under gravity: horizontal velocity stays constant while the vertical motion is free fall — treat the two directions independently with suvat.

Why it works

Once a body is in the air with only gravity acting, its horizontal and vertical motions are completely independent. Gravity acts only downwards, so it changes the vertical velocity but never the horizontal one. This is the key that unlocks every projectile problem: solve the two directions separately, linked only by the shared time

t

.

For a body projected horizontally with speed

u

from a height:

Horizontal: no force, so constant velocity — $x = ut$ .
Vertical: free fall from rest (downwards), so $y = \tfrac12 gt^2$ and $v_y = gt$ ,

taking down as positive.The path is a parabola: equal horizontal steps each second, but ever-larger vertical drops. To find when it lands, use the vertical equation with the drop height; that time then gives the horizontal range through

x = ut

. The landing speed combines the two components:

v = \sqrt{v_x^2 + v_y^2}

, with

v_x = u

unchanged.