How projectile motion calculator works
A projectile launched at speed v and angle θ from level ground splits its velocity into a constant horizontal part vx = v·cos θ and a vertical part vy = v·sin θ that gravity erodes at 9.81 m/s² every second. Gravity acts only vertically, so the vertical piece is a simple up-then-down trip: the projectile rises for vy/g seconds, stops, and falls back for the same time.
That picture gives the three headline numbers directly. Flight time is t = 2v·sin θ/g. Maximum height is H = (v·sin θ)²/(2g) — the kinetic energy of the vertical component converted to potential energy at the apex. Range is R = v²·sin(2θ)/g, which compresses both components into one expression: the double angle sin(2θ) is why complementary angles (30° and 60°, say) land at the same spot.
The calculator also reports the component velocities, the apex time (exactly half the flight), and the impact state — with no drag, the landing speed equals the launch speed and the impact angle mirrors the launch angle. The model is the physics-class ideal: level launch and landing height, no air resistance, flat Earth. A 45° launch maximises range, since sin(2 × 45°) = sin 90° = 1.