Physics-
General
Easy

Question

A man wants to reach point B on the opposite bank of a river flowing at a speed as shown in figure. What minimum speed relative to water should the man have so that he can reach point B? In which direction should be swim?

  1. u square root of 2    
  2. u divided by square root of 2    
  3. 2u    
  4. u divided by 2    

The correct answer is: u divided by square root of 2


    Let v be the speed of boatman is still water.

    Resultant of v and u should be along A B. Components of stack v with rightwards arrow on top subscript b end subscript (absolute velocity of boatman)along x and y direction are,
    v subscript x end subscript equals u minus v blanksintheta
    Further, tan invisible function application 45 degree equals fraction numerator v subscript y end subscript over denominator v subscript X end subscript end fraction
    or 1=fraction numerator v blank c o s theta over denominator u minus v blank s i n theta end fraction
    v equals fraction numerator u over denominator sin invisible function application theta plus cos invisible function application theta end fraction equals fraction numerator u over denominator square root of 2 s i n invisible function application left parenthesis theta plus 45 degree right parenthesis end fraction
    v is minimum at,
    theta plus 45 degree equals 90 degree or theta equals 45 degree
    and v subscript m i n end subscript equals fraction numerator u over denominator square root of 2 end fraction

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