Physics-
General
Easy

Question

In a race for 100m dash, the first and the second runners have a gap of one metre at the mid way stage. Assuming the first runner goes steady, by what percentage should the second runner increases his speed just to win the race.

  1. 2%  
  2. 4%  
  3. More than 4%  
  4. Less than 4%  

The correct answer is: More than 4%


    Let v subscript 1 end subscript, v subscript 2 end subscript be the initial speeds of first and second runners. Let t be time by them when the first runner has completed 50m. During this time, the second runner has covered a distance equals 50 minus 1 equals 49m.
    So, t equals fraction numerator 50 over denominator v subscript 1 end subscript end fraction equals fraction numerator 49 over denominator v subscript 2 end subscript end fraction (i)
    Suppose, the second runner increases his speed to v subscript 3 end subscript so that he covers the remaining distance left parenthesis equals 51m) in times t. So
    t equals fraction numerator 51 over denominator v subscript 3 end subscript end fraction equals fraction numerator 49 over denominator v subscript 2 end subscript end fraction
    or v subscript 3 end subscript equals fraction numerator 51 over denominator 49 end fraction v subscript 2 end subscript
    or v subscript 3 end subscript equals open parentheses 1 plus fraction numerator 2 over denominator 49 end fraction close parentheses v subscript 2 end subscript or fraction numerator v subscript 3 end subscript over denominator v subscript 2 end subscript end fraction minus 1 equals fraction numerator 2 over denominator 49 end fraction
    or fraction numerator v subscript 3 end subscript minus v subscript 2 end subscript over denominator v subscript 2 end subscript end fraction equals fraction numerator 2 over denominator 49 end fraction
    or % increase equals fraction numerator 2 over denominator 49 end fraction cross times 100 equals 4.1%

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