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Physics

Fluid-Mechanics

Easy

Question

A water barrel stands on a table of height h. If a small hole is punched in the side of the barrel at its base, it is found that the resultant stream of water strikes the ground at a horizontal distance R from the table. What is the depth of water in the barrel?

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

The correct answer is: $fraction numerator R squared over denominator 4 h end fraction$

$table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell v equals square root of 2 g d end root end cell row cell space of 1em h equals 1 half g t squared space of 1em text or end text space of 1em t equals square root of fraction numerator 2 h over denominator g end fraction end root end cell row cell therefore space of 1em R equals v t equals square root of left parenthesis 2 g d right parenthesis end root square root of fraction numerator 2 h over denominator g end fraction end root equals 2 square root of d h end root space of 1em text (Using end text end cell row cell therefore space of 1em R squared equals 4 d h text or end text d equals fraction numerator R squared over denominator 4 h end fraction end cell end table$

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