Projectile Motion Simulator
How to use the projectile motion simulator
- Set the launch speed, angle and height. The projectile launches at once; the dashed line is the path it would follow with no air.
- Change gravity to see the same throw on the Moon or Mars, and add air resistance to see how much it shortens the range.
- Drag on the picture to turn it, scroll or pinch to zoom, and drag with the right button (or two fingers) to move it. Pause stops the clock; Reset starts the simulation again with the current settings.
Frequently asked questions
Which angle gives the longest range?
45° when launching from the ground with no air. From a height the best angle is a little less than 45°, and with air resistance it is lower still, around 30 to 40° for a ball.
How is the range worked out?
Without air, the flight time is t = (v sin θ + √((v sin θ)² + 2gh)) ÷ g and the range is v cos θ × t. With air resistance there is no simple formula, so the simulation steps the motion forward in small time intervals, which is also how the dashed and solid paths come to differ.
Why does the ball go so much further on the Moon?
Range is proportional to 1 ÷ g for the same launch. The Moon's gravity is 1.62 m/s², a sixth of Earth's, so the same throw goes six times as far and takes six times as long.
It says WebGL is turned off.
The 3D view needs WebGL, which every current browser has. It can be switched off by hardware acceleration being disabled in the browser settings, or by a very old graphics driver. Turn hardware acceleration on, or try another browser.
Is anything uploaded?
No. The simulation is drawn by your own browser with WebGL; nothing is sent anywhere, and it keeps working offline once the page has loaded.