EQUATION

Velocity Decomposition

Splits a launch velocity into independent horizontal and vertical components

§ 01

The equation

EQ.VELOCITY-DECOMPOSITION

v_x = v_0\cos\theta,\; v_y = v_0\sin\theta

§ 02

What it solves

Splits a launch velocity into independent horizontal and vertical components. Once decomposed, horizontal and vertical motions can be analyzed separately using the 1D kinematic equations.

§ 03

When to use it

Any projectile problem where the launch angle is given. Also applies to any 2D motion problem where a vector must be resolved into Cartesian components.

§ 04

When NOT to use it

Not needed for purely horizontal or vertical launches (angle is 0° or 90°). In 3D problems you need a third component; in curved-surface problems, align axes with the surface normal, not horizontal/vertical.

§ 05

Common mistakes

Swapping sin and cos — v_x uses cos θ (adjacent/hypotenuse) and v_y uses sin θ (opposite/hypotenuse). Using degrees in the trig functions without converting to radians when required. Applying the same θ to both components without verifying the angle is measured from the horizontal.

§ 06

Topics that use this equation

vectors and projectile motion