A tank is filled with water upto a height H. Water is...

A tank is filled with water upto a height $H$. Water is allowed to come out of a hole $P$ in one of the walls at a depth $D$ below the surface of water. Express the horizontal distance $x$ in terms of $H$ and $D$ (a) $x=\sqrt{D(H-D)}$ (b) $x=\sqrt{\frac{D(H-D)}{2}}$ (c) $x=2 \sqrt{D(H-D)}$ (d) $x=4 \sqrt{D(H-D)}$

A tank is filled with water upto a height $H$. Water is allowed to come out of a hole $P$ in one of the walls at a depth $D$ below the surface of water. Express the horizontal distance $x$ in terms of $H$ and $D$
(a) $x=\sqrt{D(H-D)}$
(b) $x=\sqrt{\frac{D(H-D)}{2}}$
(c) $x=2 \sqrt{D(H-D)}$
(d) $x=4 \sqrt{D(H-D)}$

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Key Concepts

Torricelli's Law

Torricelli's law states that the speed of fluid flowing out of an opening under gravity is given by v = ?(2g?h), where ?h is the vertical distance from the free surface to the opening. This principle is derived from Bernoulli’s equation and energy conservation in fluids, and it provides the initial horizontal velocity of the water exiting the tank.

Projectile Motion

Projectile motion refers to the two-dimensional motion of an object under the influence of gravity. After the water exits the hole with an initial horizontal velocity, its subsequent trajectory is a parabola as it experiences vertical acceleration due to gravity while moving horizontally at constant speed.

Kinematics of Free Fall

Kinematics of free fall involves the motion of objects under the sole action of gravity. It is used to calculate the time it takes for the water to fall from the level of the hole to the ground, allowing determination of the horizontal distance traveled during that time.

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