Horizontal Projectile Motion
Overview
A projectile launched horizontally has two independent motions: horizontal — constant velocity (no acceleration, air resistance ignored); vertical — free fall with g = 9.81 m/s² downward. Treat each axis separately using the same time t. Horizontal: x = v₀t. Vertical: y = ½gt². The actual path is a parabola.
Independence of horizontal and vertical motion
The key principle: horizontal and vertical motions are completely independent of each other. Horizontally, there is no force (ignoring air resistance), so the horizontal velocity v_x = v₀ remains constant throughout the flight. Vertically, gravity acts downward with a = g = 9.81 m/s², causing the vertical velocity to increase downward. Both motions share the same time t.
Setting up the equations
For a horizontal projectile (launched horizontally with speed v₀ from height h): Horizontal: x = v₀ · t (constant velocity). Vertical: y = ½gt² (free fall from rest vertically). Time of flight from height h: t = √(2h/g). Horizontal range: R = v₀ · t. Velocity at any time: v_x = v₀ (constant), v_y = g · t. Total speed: v = √(v_x² + v_y²). Angle below horizontal: θ = arctan(v_y / v_x).
- ⚠Thinking g affects horizontal motion — it does NOT (air resistance ignored)
- ⚠Mixing up x and y equations — always label your axes clearly
- ⚠Forgetting that the initial vertical velocity is 0 for a horizontal launch
- ⚠Calculating speed (scalar) instead of velocity (vector) when direction is asked for