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Physics-

General

Easy

Question

A boat crosses a river from port $A$ to port $B$ , which are just on the opposite side. The speed of the water is $V subscript W end subscript$ and that of boat is $V subscript B end subscript$ relative to still water. Assume $V subscript B end subscript equals 2 V subscript W end subscript$ . What is the time taken by the boat, if It has to cross the river directly on the $A B$ line

$\frac{2 D}{V_{B} \sqrt{3}}$
$\frac{\sqrt{3} D}{2 V_{B}}$
$\frac{D}{V_{B} \sqrt{2}}$
$\frac{D \sqrt{2}}{V_{B}}$

The correct answer is: $fraction numerator 2 D over denominator V subscript B end subscript square root of 3 end fraction$

From figure, $V subscript B end subscript sin invisible function application theta equals V subscript W end subscript$
$sin invisible function application theta equals fraction numerator V subscript W end subscript over denominator V subscript B end subscript end fraction equals fraction numerator 1 over denominator 2 end fraction rightwards double arrow theta equals 30 degree blank left square bracket because V subscript B end subscript equals 2 V subscript W end subscript right square bracket$
Time taken to cross the river,
$t equals fraction numerator D over denominator V subscript B end subscript cos invisible function application theta end fraction equals fraction numerator D over denominator V subscript B end subscript cos invisible function application 30 degree end fraction equals fraction numerator 2 D over denominator V subscript B end subscript square root of 3 end fraction$

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