Live physics lab

Projectile Motion Simulator

Launch tennis balls, baseballs, golf balls and cannonballs and compare their flights. Set the angle, speed and height, choose gravity from Earth to the Moon, switch air resistance and wind on or off, and see range, maximum height and flight time worked out next to the textbook formulas.

RANGE–
MAX HEIGHT–
FLIGHT TIME–

Tip: drag the yellow arrow at the launcher to set angle and speed. Enter or L launches, F full screen.

How the simulation works
  1. Gravity pulls the projectile down with acceleration g. Without air, horizontal speed never changes, so the path is a parabola.
  2. Air resistance pushes against the motion relative to the air: F = ½·ρ·Cd·A·v². Light, large objects slow down most.
  3. Wind moves the air, so drag pushes the projectile along with the wind.
  4. The motion is calculated in tiny time steps (Runge–Kutta 4) and the landing point is found exactly where the path crosses the ground.
  5. No-air formulas from height h: T = (v·sinθ + √((v·sinθ)² + 2gh)) / g, range = v·cosθ·T, max height = h + (v·sinθ)²/(2g).

Spin, lift and changing air density are not included. Everything runs in your browser.

Using Projectile Motion Simulator

Launch balls, cannonballs and golf balls and compare their trajectories. Set the angle, speed, launch height, gravity and air resistance, and see range, maximum height and flight time — with the formulas worked out.

  1. Set the launch angle and speed with the sliders, or drag the launcher's arrow on the canvas.
  2. Choose a planet for gravity and an object (or your own mass, size and drag) for air resistance; add wind if you like.
  3. Press Launch. Every shot leaves its path so you can compare several at once.
  4. Read range, maximum height, flight time and impact speed for each shot, with the no-air formulas for comparison.
  5. Try Target practice, or a preset like Best angle, Moon vs Earth or Baseball with air. Download the shots as CSV.

Example

Without air, 45° gives the longest range on flat ground, and 30° and 60° land at the same spot.
With air resistance a baseball flies much shorter and its best angle drops below 45°.

Questions & answers

What is projectile motion?

The path of an object thrown through the air, pulled down only by gravity (and slowed by air). Horizontal speed stays constant without air, while vertical speed changes by g every second, which makes a parabola.

What are the formulas without air resistance?

Range R = v² sin(2θ)/g, maximum height H = v² sin²θ/(2g) and flight time T = 2v sinθ/g when launching from ground level. The simulator shows these next to its numerical results.

Why is 45° the best angle?

On flat ground with no air, sin(2θ) is largest at 2θ = 90°. From a height, or with air resistance, the best angle is lower — try it.

How is air resistance calculated?

Drag force F = ½·ρ·C_d·A·v², opposite to the motion relative to the air (including wind). ρ is air density, C_d the drag coefficient and A the cross-section area.

Can I change gravity?

Yes: Earth 9.81, Moon 1.62, Mars 3.71, Jupiter 24.79 m/s² or any custom value.

How accurate is it?

Motion is integrated with small time steps (RK4), so results match the formulas to within millimetres when air is off.

Can I export the results?

Download a CSV with every shot's settings and results, or a PNG snapshot.

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