Projectile Speed and Angle from Altitude and Distance

Find the launch speed and angle from a known peak height and horizontal range, with flight time and a trajectory sketch.

Input

Enter the peak height and horizontal range to back out the launch speed and angle needed.

Maximum height h

Height of the trajectory peak in meters

Horizontal range R

Horizontal distance from launch to landing in meters

Gravity uses the standard value g = 9.80665 m/s² and air resistance is ignored.

Launch speed v0

28.009498m/s

Launch angle θ

45deg

Flight time

4.03924 s

Time to peak

2.01962 s

Launch speed (km/h)

100.834194 km/h

Horizontal speed

19.805706 m/s

Vertical speed

19.805706 m/s

The angle comes from tanθ = 4h ÷ R and the speed from v0 = √(2gh) ÷ sinθ. Flight time is T = 2√(2h ÷ g).

From the peak height h and horizontal range R, this tool back-solves the launch speed and angle for projectile motion with no air resistance.
The angle comes from tan of theta equals 4h divided by R, and the speed is the square root of 2gh divided by the sine of the angle.
Flight time equals 2 times the square root of 2h divided by g, and the time to reach the peak is half of that.
Gravity uses the standard value g equals 9.80665 m per second squared, with launch and landing at the same height.

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