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Question: A tank is filled with water up to a height H. Water is allowed to come out of a hole P in one of the...

A tank is filled with water up to 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=D(H−D)x = \sqrt{D(H - D)}

B

x=D(H−D)2x = \sqrt{\frac{D(H - D)}{2}}

C

x=2D(H−D)x = 2\sqrt{D(H - D)}

D

x=4D(H−D)x = 4\sqrt{D(H - D)}

Answer

x=2D(H−D)x = 2\sqrt{D(H - D)}

Explanation

Solution

Time taken by water to reach the bottom

= t=2(H−D)gt = \sqrt{\frac{2(H - D)}{g}}

and velocity of water coming out of hole,

v=2gDv = \sqrt{2gD}

∴ Horizontal distance coveredx=v×tx = v \times t

= 2gD×2(H−D)g\sqrt{2gD} \times \sqrt{\frac{2(H - D)}{g}}= 2D(H−D)2\sqrt{D(H - D)}