A water barrel having water up to a depth d i | vedclass

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(C) The velocity of efflux of the liquid from the hole at the bottom is given by Torricelli's law: $v = \sqrt{2gd}$.The vertical height through which

Vedclass · Accepted Answer

$\frac{R^2}{4 h}$

Vedclass · Answer

(C) The velocity of efflux of the liquid from the hole at the bottom is given by Torricelli's law: $v = \sqrt{2gd}$.The vertical height through which the water falls is $h$.The time taken $t$ for the water to reach the ground is given by the equation of motion $h = \frac{1}{2}gt^2$,which gives $t = \sqrt{\frac{2h}{g}}$.The horizontal range $R$ is the product of the horizontal velocity and the time of flight:$R = v 	imes t$$R = \sqrt{2gd} 	imes \sqrt{\frac{2h}{g}}$$R = \sqrt{2gd 	imes \frac{2h}{g}}$$R = \sqrt{4dh}$Squaring both sides,we get $R^2 = 4dh$.Therefore,$d = \frac{R^2}{4h}$.

$A$ water barrel having water up to a depth $d$ is placed on a table of height $h$. $A$ small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel,then the value of $d$ is

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