Q 11-09-018NEETJEE MainTop questionHard
A tank standing on the ground is filled with water to a height $H$. A small hole is to be made in its side so that the water jet lands as far from the tank as possible. The hole should be at a height above the ground of
Answer: (A) $\dfrac{H}{2}$
For a hole at height $h$, the depth below the surface is $H - h$, so the jet speed is $v = \sqrt{2g(H - h)}$.
The jet takes time $t = \sqrt{2h/g}$ to fall, so the range is $x = vt = 2\sqrt{h(H - h)}$.
$h(H - h)$ is largest when $h = \dfrac{H}{2}$, giving a maximum range of $H$.
Solution by Sreeraj P, M.Sc Physics