Projectile Initial Speed Calculator (Angle and Peak Height)
Find the launch speed, range, and flight time from the launch angle and maximum height. Shows the trajectory.
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Input
Enter the launch angle and maximum height to compute the required initial speed and related values.
deg
An angle greater than 0 and less than 90 degrees
m
The peak height reached on the trajectory
The standard gravity g = 9.80665 m/s squared is used.
Result
Required initial speed v0
19.805706m/s
Range R
40 m
Flight time T
2.856174 s
Initial speed (per hour)
71.300542 km/h
Horizontal speed vx
14.004749 m/s
Vertical speed vy
14.004749 m/s
v0 = sqrt(2 g h) / sin(theta); range R = v0 squared times sin(2 theta) / g; flight time T = 2 v0 sin(theta) / g. Air resistance is ignored.
How it works
- The maximum height h is set by the vertical launch speed vy = v0 sin(theta), giving h = (v0 sin(theta)) squared divided by (2 g).
- Solving for the initial speed gives v0 = sqrt(2 g h) divided by sin(theta).
- The flight time is T = 2 v0 sin(theta) / g and the range is R = v0 squared times sin(2 theta) / g.
- Air resistance is ignored and launch from level ground is assumed. The standard gravity g = 9.80665 m/s squared is used.
- Enter a launch angle greater than 0 and less than 90 degrees, and a positive maximum height.
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