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About this tool
Interactive physics simulator for projectile trajectories with real-time vectors, gravity presets, air resistance, and trajectory analytics.
The Projectile Motion Simulator launches a projectile at a chosen angle and speed and draws its path against the vacuum equations of 2D kinematics — range R = v₀²·sin2θ/g, peak height H = (v₀·sinθ)²/2g and flight time T = 2v₀·sinθ/g — while animating the horizontal and vertical velocity vectors as it flies. Switch on air resistance and it integrates a quadratic drag force, F_d = ½·C_d·v², with Euler steps of 0.03 s, drawing the real trajectory against the dashed ideal one so the gap between them is visible. It is built for physics students and teachers who want the formulas and the picture side by side.
Open Projectile Motion Simulator on AltFTool — it loads instantly in your browser.
Under Launch Parameters drag Launch Angle across 0-90° and Initial Velocity across 5-100 m/s, then pick an Environment Gravity preset: Earth (9.81m/s²), Moon (1.62m/s²), Mars (3.71m/s²) or Jupiter (24.79m/s²).
Tick Air Resistance Drag and set the Drag Coefficient between 0.01 and 0.5, then press Launch; the ball is drawn with a red Vx Vector, a green Vy Vector and an amber Resultant V arrow, and Pause halts it.
'Telemetry & Real-Time Stats' gives Max Height, Total Range and Flight Time from the vacuum formulas plus live Current Speed, while the solid trail falls short of the dashed ideal parabola; Reset clears the trail.
The dashed vacuum parabola stays on screen while the drag-affected trail is drawn over it, so the shortfall is measured, not described.
Four presets — Earth 9.81, Moon 1.62, Mars 3.71 and Jupiter 24.79 m/s² — plus a free g value, so the same launch can be replayed under any of them.
Horizontal, vertical and resultant velocity arrows are drawn at the projectile each frame, which is where the 'vy reaches zero at the apex' idea becomes obvious.
45 degrees, in a vacuum. Range is v₀²·sin2θ/g and sin2θ peaks at 1 when θ = 45 degrees, so any other angle travels less at the same speed. With air resistance switched on the optimum drops below 45 degrees, which you can see by comparing runs.
Launch angle from 0 to 90 degrees, initial speed from 5 to 100 m/s, and a drag coefficient from 0.01 to 0.5 with a mass in kilograms. Gravity comes from the four planet presets or any value you enter.
No — those three figures are always the vacuum results from the standard formulas, so they act as the ideal benchmark. When drag is on, the actual flight falls short of them, and the difference is what the solid trail against the dashed curve shows.
It is a teaching approximation, not an aerodynamics tool. Drag is modelled as a quadratic force opposing velocity and integrated with forward Euler steps of 0.03 s, so it captures the shape of the effect — a shortened, asymmetric arc with a steeper descent — but it folds air density and cross-sectional area into one coefficient and accumulates step error over long flights.