How it works
A projectile launched horizontally from a height has two independent motions: it keeps its horizontal speed unchanged while gravity accelerates it downward. The vertical drop alone sets the flight time — t = √(2h/g), exactly the free-fall time for that height — and the horizontal range is just that time multiplied by the launch speed: R = v·√(2h/g).
Because the fall time depends only on the height, a fast and a slow projectile launched from the same table hit the floor at the same instant; the faster one simply lands further away. Double the launch speed and you double the range; quadruple the height and the range only doubles, since range grows with the square root of height.
The impact speed combines the unchanged horizontal component with the vertical speed gained in the fall (v_y = g·t), so it is √(v² + (g·t)²) — always faster than the launch speed. This calculator assumes a horizontal launch, no air resistance, and g ≈ 9.81 m/s². For an angled launch on level ground, use the projectile motion calculator.
Use it in real life
Ski jumps and stunts: a ramp that leaves you moving horizontally sends you along exactly this path — the take-off speed sets how far you fly, the drop height sets how long you are airborne.
Water jets and fountains: a hose held level off a wall throws water in this parabola; the range is the free-fall time from that height times the exit speed.
Physics labs: rolling a ball off a table and measuring where it lands is the classic way to recover its launch speed — measure the range and height, then invert R = v·√(2h/g).
Frequently asked questions
How do you find the range of a horizontal projectile?
First get the fall time from the height, t = √(2h/g), then multiply by the horizontal launch speed: R = v·√(2h/g). The horizontal speed never changes, so range is simply speed times time in the air.
Does launch speed affect how long the projectile is in the air?
No. For a horizontal launch the time aloft depends only on the drop height, not the speed. Two balls leaving a table at different speeds land at the same moment — the faster one just lands further out.
Why is the impact speed higher than the launch speed?
The horizontal speed stays constant while gravity adds a vertical speed v_y = g·t during the fall. The two combine as √(v² + v_y²), so the object always lands faster than it was launched.