For a ground-to-ground projectile of launch angle θ and range R, the slope of the tangent to its trajectory at x=R/4 is:
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Question

For a ground-to-ground projectile of launch angle θ and range R, the slope of the tangent to its trajectory at x=R/4 is:

G1 Physics · Accepted Answer

The trajectory is y=x tanθ(1−x/R). Therefore dy/dx = tanθ(1−2x/R). At x=R/4, dy/dx = tanθ(1−1/2) = tanθ/2.