Question

The height of water level in a tank is $H=100\text{cm}$. The water stream is coming out of a hole at the depth of $20\text{cm}$ from top surface of water. Find out the time taken by the water coming out of the hole to reach the ground and the horizontal range of water. (Take $g=1000{\text{cm/s}}^2$)

• A. $0.4\text{sec},80\text{cm}$
• B. $0.4\text{sec},90\text{cm}$
• C. $0.2\text{sec},80\text{cm}$
• D. $0.2\text{sec},90\text{cm}$

Answer 1

The correct option is A $0.4\text{sec},80\text{cm}$

Given, height of hole from the upper surface of water, $h=20\text{cm}$
So, velocity of efflux, $v=\sqrt{2gh}=\sqrt{2\times 1000\times 20}$
$v=200\text{cm/s}$
The height of hole from ground, $H^{\prime }=100-20=80\text{cm}$
The time taken by the water coming out of the hole to reach the ground, $t=\sqrt{\frac{2H^{\prime }}{g}}=\sqrt{\frac{2\times 80}{1000}}$
$t=0.4\text{sec}$
Now, horizontal range of water $=v\times t=200\times 0.4=80\text{cm}$