How this calculator works
The two velocity components evolve independently under constant gravity: horizontal velocity is unchanged and vertical velocity decreases linearly. The flight ends at the landing plane. The observation can be specified by elapsed time or horizontal distance. A measured range can determine launch speed if angle and initial height are known. This is a point-particle model without drag, wind, spin, bounce or terrain.
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.