Here is question: A tall building stands on level ground. The nozzle of a water sprinkler is positioned point P on the ground at a distance d from a wall of the building. Water sprays from nozzle with speed V and the nozzle can be pointed in any direction from P.

Suppose that V = 2sqrt(gd). Show that the portion of wall that can be sprayed with water is a parabolic segment of height (15/8)d and area (5/2)d^2sqrt15.

So for first bit of height. Ive achieved that, but used optimization to find maximum height. Is that a correct interpretation of question?

Sub v = 2 Sqrt(gk) and x = k into

gx^2(tan a)^2 - 2v^2k(tan a) - 2v^2y + gk^2 = 0 (a is angle)

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dy/da = k(seca)^2 - k/4tana(seca)^2

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tana = 4

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Also second bit to find area,how do i prove that segment is parabolic? And then how do we attempt to solve it? Do i have to find equation of parabola? Or can i use simpson's rule?