If R is the horizontal range of a ground-to-ground projectile, its trajectory can be written as:
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Question

If R is the horizontal range of a ground-to-ground projectile, its trajectory can be written as:

G1 Physics · Accepted Answer

The standard trajectory is y = x tanθ − gx²/(2u²cos²θ). Also R = u²sin2θ/g = 2u²sinθcosθ/g. Therefore g/(2u²cos²θ) = tanθ/R. Hence y = x tanθ − x²tanθ/R = x tanθ(1−x/R).