Question

A water hose pipe of cross-section area $5c{m}^2$ is used to fill a tank of $120L$. It has been observed that it takes $2min$ to fill the tank. Now, a nozzle with an opening of cross-section area $1c{m}^2$ is attached to the hose. The nozzle is held so that water is projected horizontally from a point $1m$ above the ground. The horizontal distance over which the water can be projected is (Take $g=10m/s^2)$ :

• A. $3m$
• B. $8m$
• C. $4.47m$
• D. $8.64m$

Answer 1

Answer: (C)

$4.47m$

Volume flow rate$=av=\frac{V}{t}$
$\therefore$ $v_1=\frac{V}{A_{1}t}=\frac{120\times {10}^{-3}}{5\times {10}^{-4}\times 2\times 60}=2$
Now, $A_1{v}_1=A_2{v}_2$
$A_2$ is $\frac{1}{5}$th of $A_1$
Hence $v_2$ is five times of $v_1$ or 10 m/s
$t_0=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\times 1}{10}}=0.447$ s
$R=v_2{t}_0=4.47$ m