How to use it
- Enter the Launch speed in m/s, the Launch angle in degrees above the horizontal (negative to throw downward) and the Launch height in metres.
- Keep gravity at 9.81 m/s2 or tap a preset such as Moon.
- Read the range, maximum height, flight time and landing speed; the chart shows the path.
How it works
The horizontal speed is constant, vx = v cos(angle). The height follows y(t) = h + vy t - g t^2 / 2 with vy = v sin(angle). Setting y to zero gives the flight time, and the range is vx times that time. The peak is at t = vy / g when the object rises. The chart uses the same scale on both axes, so the launch angle looks true.
Worked example
A ball thrown at 20 m/s at 45 degrees from the ground on Earth: vy = 14.14 m/s, flight time 2.88 s, range 400 / 9.81 = 40.77 m and maximum height 200 / 19.62 = 10.19 m. On the Moon (1.62 m/s2) the same throw travels about 246.9 m.
Tips
- Doubling the launch speed multiplies the range and the height by four.
- Angles that add up to 90 degrees, such as 30 and 60, give the same range from level ground.