Question

A water tank stands on the roof of a building as shown in the figure. The value of height of water above the hole $\left(h\right)$ for which the horizontal distance covered by the water $\left(x\right)$ is maximum -

• A. $0.5\text{m}$
• B. $0.8\text{m}$
• C. $1\text{m}$
• D. $0.2\text{m}$

Answer 1

The correct option is C $1\text{m}$

We know that speed of efflux is given by, $v=\sqrt{2gh}$
$\Rightarrow v=\sqrt{20h}$ .........(1)


For vertical motion,
$s=ut+\frac{1}{2}g{t}^2$
$4-h=\frac{1}{2}\times 10\times t^2$ [ from figure ]
$t=\sqrt{\frac{4-h}{5}}$ ...........(2)
For horizontal range of water,
$x=vt$
$x=\sqrt{4h(4-h)}$ [ from (1) and (2) ]
On differentiating both side with respect to $h$
$\frac{dx}{dh}=\frac{1}{2\left(\sqrt{4h(4-h}\right)}.(16-8h)$
For maximum value of $x$
$\frac{dx}{dh}=0$
$\Rightarrow h=2$ and $h\ne 0,4$
But permitted value of $h$ is from $0$ to $1\text{m}$
$\therefore h=1$ for maximum value of $x$