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(A) The height of the water level above the hole is $D$. The height of the hole above the ground is $(H-D)$.Using Torricelli's law,the velocity of the

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$2\sqrt{D(H-D)}$

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(A) The height of the water level above the hole is $D$. The height of the hole above the ground is $(H-D)$.Using Torricelli's law,the velocity of the water jet emerging from the hole is $v = \sqrt{2gD}$.The time $t$ taken by the water jet to reach the ground from the height $(H-D)$ is given by the equation of motion $S = ut + \frac{1}{2}at^2$,where $S = H-D$,$u = 0$,and $a = g$.$H-D = 0 + \frac{1}{2}gt^2 \implies t = \sqrt{\frac{2(H-D)}{g}}$.The horizontal distance $x$ (range) is the product of horizontal velocity and time:$x = v 	imes t = \sqrt{2gD} 	imes \sqrt{\frac{2(H-D)}{g}}$.$x = \sqrt{2gD 	imes \frac{2(H-D)}{g}} = \sqrt{4D(H-D)} = 2\sqrt{D(H-D)}$.

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