Horizontal Projectile Motion Calculator

Horizontal projectile motion describes an object that leaves an elevated surface with velocity directed parallel to the ground. In the ideal kinematics model, horizontal and vertical motion are independent. No horizontal acceleration acts after launch, so the horizontal component of velocity remains constant. Gravity accelerates the object downward at the selected rate. Combining those perpendicular motions produces the familiar curved, parabolic trajectory. The calculator first determines flight time from the vertical drop. Because initial vertical velocity is zero, height equals one half times gravitational acceleration times time squared. Solving gives time as the square root of twice the height divided by gravity. Horizontal range is then launch speed multiplied by that flight time. Vertical impact speed equals gravity multiplied by time, while final speed is the magnitude of the horizontal and vertical velocity components found with the Pythagorean relationship. This separation explains an important result: in the ideal model, launch speed does not change the time needed to reach the ground. An object dropped from rest and an object projected horizontally from the same height land together, provided both begin simultaneously and experience the same gravity. Increasing horizontal speed only increases range and the horizontal contribution to final speed. Increasing height gives gravity more time to act, increasing flight time, range, and downward impact speed. Real projectiles can differ because drag depends on shape, frontal area, air density, wind, and speed. Earth curvature, changing elevation, lift, spin, and a nonuniform gravitational field may also matter over long distances. The calculator assumes level ground directly below the launch point, constant gravity, no air resistance, and no initial vertical velocity. It is suitable for classroom problems, quick estimates, demonstrations, and checking hand calculations. Use meters, seconds, and meters per second together. Standard Earth gravity near sea level is approximately 9.81 m/s², but the editable gravity field allows comparisons with other planets or simplified textbook values such as 9.8 or 10 m/s². Height must represent the vertical distance from launch point to landing level, not the length of a ramp or the path traveled by the projectile.