Question

A tank is filled with water upto a height H. Water is allowed to come out of a hole P in one of the walls at a depth h below the surface of water as shown in figure. Express the horizontal distance X in terms of H and h

• A. $X=\sqrt{h(H-h)}$
• B. $X=\sqrt{\frac{h}{2}(H-h)}$
• C. $X=2\sqrt{h(H-h)}$
• D. $X=4\sqrt{(H-h)}$

Answer 1

The correct option is C $X=2\sqrt{h(H-h)}$

Vertical distance covered by water before striking ground =(H-h)
Time taken is
t = $\sqrt{2(H-h).g}$
Horizontial velocity of water coming out of hole at P
u = $\sqrt{2gh}$
Therefore horizontal range
= ut
= $\sqrt{2gh}\times \sqrt{\frac{2(H-h)}{g}}$
= $2\sqrt{h(H-h)}$