Question

Water is filled in a tank upto $4\text{m}$ height. The base of the tank is at height $1\text{m}$ above the ground. At what height should the hole be made from the ground, so that the water can be sprayed upto maximum horizontal distance on ground?

• A. $2\text{m}$
• B. $2.5\text{m}$
• C. $1.5\text{m}$
• D. $3\text{m}$

Answer 1

The correct option is B $2.5\text{m}$

Let the height of hole from the base of container be h.
So, velocity of efflux$=\sqrt{2g(4-h)}$



Now, Range of liquid, $R=v\times t$
$R=\sqrt{2g(4-h)}\times \sqrt{\frac{2(h+1)}{g}}$
$\Rightarrow R=2\sqrt{(h+1)(4-h)}$
$\Rightarrow R=2(-h^2+3h+4{)}^{1/2}$
Differentiating w.r.t $h$, we get
$\frac{dR}{dh}=2\times \frac{1}{2}(-h^2+3h+4{)}^{-1/2}(-2h+3)$
For maximum Range, Put $\frac{dR}{dh}=0$
$(-2h+3)=0$
$\Rightarrow h=\frac{3}{2}=1.5\text{m}$
$\therefore$ Height of the hole from the ground $=1+1.5=2.5\text{m}$