Interactive projectile motion visualisation using vector methods
One Vector Equation Replaces All Those Formulae
Traditional projectile motion drowns you in separate horizontal and vertical equations. Vector methods compress everything into one truth: constant downward acceleration. Integrate twice and you've solved the entire problem. Change the launch angle and watch the range and velocity arrows respond.
Starting from a = -g ĵ (acceleration vector pointing down), integrate once to get velocity: v = v₀ + at. The initial velocity v₀ splits into horizontal and vertical components based on launch angle. Integrate again to get position: r = r₀ + v₀t + ½at². The horizontal component has zero acceleration, so it maintains constant velocity throughout the flight. The vertical component experiences constant downward acceleration g, creating the parabolic path. Time of flight comes from setting the vertical displacement to zero and solving for t. Every classic projectile result—range, maximum height, time of flight—emerges directly from these two integration steps. No memorising separate equations for x and y motion.
Know This
The acceleration vector is constant and directed downward with magnitude g—integrate it twice and you've solved projectile motion completely, with horizontal velocity remaining constant throughout the entire flight.