Projectile Range, Height, and Flight Time

ScopeLevel-ground kinematics: range R = v^2 sin(2 theta)/g, max height H = v^2 sin^2(theta)/(2g), flight time t = 2 v sin(theta)/g. An 80 ft/s stream at 45 degrees reaches 199 ft out and 50 ft up in still air; the range peaks at 45 degrees and complementary angles (30 and 60) give the same reach but different arcs - the trade between reach, height, and coverage a nozzle operator or sprinkler layout makes. Air resistance is NEGLECTED, so a real stream falls short - this is the still-air upper bound. A launch above the landing (a nozzle on a ladder, a roof edge) is an input, and the page gives the angle for the longest reach, below 45 degrees then; wind and stream break-up are separate. A planning estimate; field conditions govern.

Formula or tablet = (v sin(theta) + sqrt((v sin(theta))^2 + 2 g h))/g; R = v cos(theta) t; H = v^2 sin^2(theta)/(2g) above the launch; best angle = atan(v/sqrt(v^2 + 2 g h)); g = 32.174 ft/s^2. On level ground (h = 0) R = v^2 sin(2 theta)/g, peaking at 45 deg with complementary angles giving equal range.

Source and editionThe level-ground projectile relations R = v^2 sin(2 theta)/g, H = v^2 sin^2(theta)/(2g), t = 2 v sin(theta)/g (standard kinematics), by name.

Free accessThe projectile relations are standard published kinematics; the launch speed and angle are the user's inputs.

What governsEstimate. AHJ and licensed professional govern.

API field namesvelocity_fps, angle_deg, range_ft, max_height_ft, flight_time_s

• Range/height/time R = v^2 sin(2 theta)/g, H = v^2 sin^2(theta)/(2g), t = 2 v sin(theta)/gkinematics
• Optimal angle range peaks at 45 deg; complementary angles give equal rangekinematics
• No drag still-air upper bound; air resistance shortens a real stream, launch height/wind are separatescope of this tile