Q 11-09-114JEE MainJEE Main 2021 (27 Jul, Shift 2)Easy
The water is filled up to a height of $12$ m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth $h$ below the water level. The value of $h$ for which the emerging stream of water strikes the ground at the maximum range is ______ m.
Numerical value type. Enter your answer.
Answer: 6
Efflux speed $v = \sqrt{2gh}$; the hole is at height $H - h$ above the ground, so the time of fall is $\sqrt{\dfrac{2(H - h)}{g}}$.
Range $x = 2\sqrt{h(H - h)}$, which is maximum when $h = \dfrac H2 = 6$ m.
Solution by Sreeraj P, M.Sc Physics