How this calculator works
Horizontal and vertical motions share the same flight time. With no initial vertical component, drop height determines that time through free fall. Horizontal velocity remains unchanged, so multiplying it by flight time gives range. Impact speed combines horizontal speed with the downward speed acquired during the fall. A zero-height drop has zero duration, which cannot determine a launch speed from range.
Formula
t = sqrt(2h/g); R = vx t; h = g(R/vx)^2/2; impact speed = sqrt(vx^2+(gt)^2).
Worked example
At g = 10 m/s2, a 20 m drop lasts 2 s. A horizontal launch at 3 m/s therefore travels 6 m. A 5 m drop lasts 1 s, so a 20 m range requires 20 m/s.
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Frequently asked questions
Does a faster launch delay landing?
No. Without drag, horizontal speed does not change the vertical fall time.
Can the object start upward?
Use the general projectile calculator for a nonzero vertical launch velocity.
Are the graph units adjustable?
Scalar results have unit selectors. The chart axes stay in metres so the plotted coordinates remain explicit.