Editing Projectile motion (section)

=== Velocity ===
Let the projectile be launched with an initial [[velocity]] <math>\mathbf{v}(0) \equiv \mathbf{v}_0 </math>, which can be expressed as the sum of horizontal and vertical components as follows:
:<math> \mathbf{v}_0 = v_{0x}\mathbf{\hat x} + v_{0y}\mathbf{\hat y} </math>.
The components <math> v_{0x} </math> and <math> v_{0y} </math> can be found if the initial launch angle θ is known:
:<math> v_{0x} = v_0\cos(\theta)</math>,
:<math> v_{0y} = v_0\sin(\theta)</math>

The horizontal component of the [[velocity]] of the object remains unchanged throughout the motion. The vertical component of the velocity changes linearly,{{NoteTag|decreasing when the object goes upward, and increasing when it goes downward}} because the acceleration due to gravity is constant. The accelerations in the <var>x</var> and <var>y</var> directions can be integrated to solve for the components of velocity at any time <var>t</var>, as follows:
: <math> v_x = v_0 \cos(\theta) </math>,
: <math> v_y = v_0 \sin(\theta) - gt </math>.

The magnitude of the velocity (under the [[Pythagorean theorem]], also known as the triangle law):
: <math> v = \sqrt{v_x^2 + v_y^2 } </math>.