I'm not really sure how to do this Projectile Motion question since it gives no equations of motion or anything, just a lot of text and conditions:
A tall building stands on level ground. The nozzle of a water sprinkler is positioned at a point $P$ on the ground at a distance $d$ from a wall of the building. Water sprays from the nozzle with speed $V$ and the nozzle can be pointed in any direction from $P$.
Suppose that $V=\sqrt{2gd}$.
Show that the portion of the wall that can be sprayed with water is a parabolic segment of height ${8\over 15}d$ and area ${5\over 2}d^2\sqrt{15}$.
Someone has already asked this question, but they solved it before anyone else could answer it, so I was wondering if anyone else would be able to assist me? I tried to solve this question by setting the angle in the vertical plane to a constant $\frac{\pi}{4}$ for max range, and varied the angle of the diagonal in which the trajectory of the projectile would lie in. I ended up getting a result:
$y=\sqrt{x^2+d^2} – {x^2\over 4d}$
I'm certain this isn't a parabola though so I wasn't sure what I did wrong. Could someone point out the flaw in this argument? For reference, the equation of the parabola is, I believe:
$y=-{x^2\over 8d} + {15\over 8}d$
Thanks!
Best Answer
There seems to be a typo in the problem : The $V = 2\sqrt{gd}$ and then the rest follows as given below in the solution. I think I got what the book answer is.
Solution as follows: