Physics-
General
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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

  1. fraction numerator 2 D over denominator V subscript B end subscript square root of 3 end fraction  
  2. fraction numerator square root of 3 D over denominator 2 V subscript B end subscript end fraction  
  3. fraction numerator D over denominator V subscript B end subscript square root of 2 end fraction  
  4. fraction numerator D square root of 2 over denominator V subscript B end subscript end fraction  

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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