Projectile motion: components first, formulas second

Projectile motion becomes messy when the launch speed is used as if it points in one direction. It does not; it has two components.

The main idea

Resolve the initial velocity first: $v_{0x}=v_0\cos \theta$ and $v_{0y}=v_0\sin \theta$. Then use vertical motion for time and horizontal motion for range.

A short example

At the top, vertical velocity is zero, so $0=v_0\sin \theta -gt$ gives the time to peak.

Check while you solve

• Draw the velocity triangle.
• Use $g$ only in the vertical equation.
• Do not use range until time is known.