How this calculator works
Eliminating time gives a parabolic height-versus-distance curve whenever horizontal velocity is nonzero. The path chart and coordinate table use metres and seconds, while scalar results offer unit selectors. The table includes launch and landing and 19 intermediate instants. A time or distance observation outside the free-flight interval is rejected so the displayed position stays on the plotted path.
Formula
x=vx t; y=h0+vy t-gt^2/2; vy(t)=vy-gt; T=(vy+sqrt(vy^2+2gh0))/g; y(x)=h0+(vy/vx)x-gx^2/(2vx^2).
Worked example
With vx = 8 m/s, vy = 6 m/s, h0 = 0 and g = 10 m/s2, landing is at 1.2 s and 9.6 m. At 0.6 s, the projectile is at (4.8,1.8) m with zero vertical velocity.
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Frequently asked questions
Can the graph show a vertical launch?
Yes. Its horizontal coordinates are all zero. Use a time observation because a distance observation cannot determine time.
Why does the graph stay in metres?
The plotted coordinates and axis labels use fixed SI units. Scalar outputs can be converted independently.
Can I recover speed from range?
Yes, when the entered launch angle and height admit a finite positive speed for that range.