Physics-
General
Easy

Question

A man starting from point P crosses a 4 km wide lagoon and reaches point Q in the shortest possible time by the path shown in the figure. If the person swims at a speed of 3 km/hr and walks at a speed of 4 km/hr, then his time of journey is (µsaltwater = 4/3) :

  1. 4hr, 10 min.    
  2. 4 hr and 30 min.    
  3. 3 hr and 50 min    
  4. 5 hr and 10 min.    

The correct answer is: 4hr, 10 min.


    As we know that light travels in a path such as to reach from one point to another in shortest possible time. Therefore, the man must travel along that path on which light would have travelled in moving from P to Q.

    By Snell's law ;
    fraction numerator sin invisible function application i over denominator sin invisible function application r end fraction equals fraction numerator mu subscript 2 end subscript over denominator mu subscript 1 end subscript end fraction rightwards double arrow s i n invisible function application r equals fraction numerator mu subscript 1 end subscript over denominator mu subscript 2 end subscript end fraction. s i n invisible function application i
    table row cell s i n invisible function application r equals fraction numerator 3 over denominator 5 end fraction times fraction numerator 4 over denominator 3 end fraction equals fraction numerator 4 over denominator 5 end fraction rightwards double arrow r equals 53 to the power of ring operator end exponent end cell row cell therefore A O equals 10 K m end cell end table
    From P to A :
    table row cell t subscript 2 end subscript equals fraction numerator 10 over denominator 4 end fraction equals fraction numerator 5 over denominator 2 end fraction end cell row cell T equals t subscript 1 end subscript plus t subscript 2 end subscript equals fraction numerator 5 over denominator 3 end fraction plus fraction numerator 5 over denominator 2 end fraction equals fraction numerator 25 over denominator 6 end fraction text end text text h end text text r end text text. end text text end text equals open parentheses fraction numerator 24 over denominator 6 end fraction plus fraction numerator 1 over denominator 6 end fraction close parentheses h r end cell row cell equals open parentheses 4 h r plus fraction numerator 1 over denominator 6 end fraction h r close parentheses equals 4 h r plus 10 text end text text m end text text i end text text n end text text u end text text t end text text e end text text s end text text end text end cell end table

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