Ballistics
Ballistics & firing trajectory
Visualize the ballistic parabola by cannon inclination: from 0° (flat fire) to 90° (vertical fire, zero range).
Projectile motion
x = V₀·cos(θ)·t | y = V₀·sin(θ)·t − ½·g·t²
Parabolic trajectory without air friction.
Maximum range
R = V₀² · sin(2θ) / g
Range is maximum at 45° and zero at both 0° and 90°.
Ballistic trajectory by inclination
Firing angle45°
Initial velocity V₀80 m/s
Range
652 m
Max height
163 m
Flight time
11,5 s
At 90°, horizontal range is zero: the projectile falls back vertically (dangerous). At 45°, range is maximized.