Projectile Motion Simulator — Ballistic Trajectory, Range & Apex Interactive

Interactive 3D projectile-motion laboratory with a launch fixture, adjustable speed, angle, height, gravity and mass, live trajectory and range measurements, energy charts, guided experiments, a model-verification bench, timestamped event log and a knowledge-check quiz.

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About the Projectile Motion Simulator

This simulator launches a point mass from an adjustable fixture and follows its ideal ballistic path under constant gravity, with no air resistance. Adjust launch speed, angle, height, gravity and mass, then watch the traveled trajectory, velocity vector and ground range update together with live horizontal and vertical measurements.

What the simulator shows

• A real-time 3D view of the adjustable launch fixture, the projectile with its velocity indicator arrow, the predicted full trajectory shown pale with the traveled segment highlighted bright, ground range markers and landing target, and gravity's downward direction — with home view, focus-selected-part, auto-rotate, expand and toggleable labels. • Five live controls: launch speed (5-30 m/s), launch angle (5°-85° above horizontal), launch height (0-5 m), gravitational acceleration (1.62-15 m/s²) and mass. • Run/pause the flight, advance by 0.1 s or 1 s single steps, and a playback-speed selector from slow motion to accelerated time. • Reset laboratory (relaunch) and a live sequence narrative describing what is happening during flight. • Eight live metrics: horizontal distance, height above ground, horizontal velocity, vertical velocity, speed, predicted ground range, predicted apex height and time to ground. • A Curves & measurements tab with a horizontal-distance-vs-height trajectory chart, model equations and snapshot measurements. • An Experiments tab with four guided scenarios (complementary angles, at the apex, elevated launch, lower gravity), a model-verification bench of independent automated checks, and a timestamped event log with a copyable trial report. • A Learn & assess tab with guided lessons, a two-question knowledge-check quiz and a written scope/reference statement.

Why the horizontal and vertical axes can be treated separately

With no air resistance, horizontal acceleration is zero while vertical acceleration is a constant −g, and both components share the same elapsed time. This means the horizontal velocity never changes during flight, even as the vertical velocity is continuously slowed by gravity, reaches zero at the apex, and then reverses sign on the way down.

At the apex specifically, vertical velocity passes through zero while horizontal velocity remains exactly what it was at launch — the projectile has not stopped, it has simply stopped rising for an instant. The complementary-angles experiment shows a related consequence: launching at 30° and at 60° from the same height with the same speed produces the same ground range, even though their apex heights and total flight times differ.

Reading ground-contact time, range and the model equations

The equations panel shows vx = v0 cos θ, vy(t) = v0 sin θ − gt, x(t) = vx t, y(t) = h0 + v0 sin θ t − ½gt², the general ground-contact time tground = [vy0 + √(vy0² + 2gh0)]/g, Range = vx tground, and total energy E = ½mv² + mgy. The general ground-contact formula matters because the familiar range shortcut v0² sin(2θ)/g only holds when launch and landing heights are equal — this simulator instead solves for the actual first positive ground-contact root, which is why the elevated-launch experiment shows a longer flight time than the same launch from ground level.

This is a point-mass, constant-uniform-gravity model with no air resistance or Earth curvature, and motion stops at first ground contact without modeling impact or bounce. The display also uses independent horizontal and vertical scales to keep long, flat arcs visible on screen — the physical distances belong to the live measurements, not to how far apart the drawn axes appear.

Frequently asked questions

At the apex of a projectile's flight, which velocity component is zero?

Only the vertical velocity component is zero at the apex, for any launch that is not perfectly vertical. The horizontal velocity component stays constant throughout the entire flight, since horizontal acceleration is zero with no air resistance — the projectile has momentarily stopped rising, not stopped moving.

Does mass affect the range of a projectile in this vacuum model?

No. Mass cancels out of the equations of ideal gravitational motion, so heavier and lighter projectiles launched with the same speed, angle and height follow identical trajectories and land at the same range and time. Mass does change the absolute kinetic and potential energy values shown in the measurements, since those scale directly with mass.

Why do 30° and 60° launches from the same height reach the same range?

For equal launch and landing heights, range depends on sin(2θ), and sin(2×30°) equals sin(2×60°) — both equal sin(60°). The two complementary angles therefore produce matching ranges, even though the steeper 60° launch reaches a higher apex and stays airborne longer than the flatter 30° launch, as the complementary-angles experiment demonstrates directly.

What does this projectile motion model not include?

This is a point-mass model with constant, uniform gravity and no air resistance or Earth curvature. It excludes drag, spin effects such as the Magnus force, wind, and any impact or bounce behavior — the simulated flight simply stops at the first ground-contact point. The displayed trajectory also uses independent horizontal and vertical display scales to keep long arcs visible; physical distances should be read from the live measurements rather than the drawing proportions.

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