A horizontal line is drawn at height 3H/4, where H is the maximum height of a ground-to-ground projectile. The horizontal distance between the two points where this line cuts the trajectory is:
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A horizontal line is drawn at height 3H/4, where H is the maximum height of a ground-to-ground projectile. The horizontal distance between the two points where this line cuts the trajectory is:

G1 Physics · Accepted Answer

Use the normalized trajectory y/H = 4ξ(1−ξ), where ξ=x/R. Set 3/4 = 4ξ(1−ξ). This gives 16ξ²−16ξ+3=0. Hence ξ=1/4 or 3/4. Therefore the horizontal separation is R(3/4−1/4)=R/2.