Physics-
General
Easy

Question

A stone dropped from a building of height h and it reaches after t seconds on earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after t subscript 1 end subscript and t subscript 2 end subscript seconds respectively, then

  1. t equals t subscript 1 end subscript minus t subscript 2 end subscript  
  2. t equals fraction numerator t subscript 1 end subscript plus t subscript 2 end subscript over denominator 2 end fraction  
  3. t equals square root of t subscript 1 end subscript t subscript 2 end subscript end root  
  4. t equals t subscript 1 end subscript superscript 2 end superscript t subscript 2 end subscript superscript 2 end superscript  

The correct answer is: t equals square root of t subscript 1 end subscript t subscript 2 end subscript end root


    If a stone is dropped from height h then
    h equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent(i)
    if a stone is thrown upward with velocity u then
    h equals negative u blank t subscript 1 end subscript plus fraction numerator 1 over denominator 2 end fraction g t subscript 1 end subscript superscript 2 end superscript(ii)
    If a stone is thrown downward with velocity u then
    h equals u t subscript 2 end subscript plus fraction numerator 1 over denominator 2 end fraction g t subscript 2 end subscript superscript 2 end superscript(iii)
    From (i) (ii) and (iii) we get
    negative u t subscript 1 end subscript plus fraction numerator 1 over denominator 2 end fraction g t subscript 1 end subscript superscript 2 end superscript equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent(iv)
    u t subscript 2 end subscript plus fraction numerator 1 over denominator 2 end fraction g t subscript 2 end subscript superscript 2 end superscript equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent(v)
    Dividing (iv) and (v) we get
    therefore fraction numerator negative u t subscript 1 end subscript over denominator u t subscript 2 end subscript end fraction equals fraction numerator fraction numerator 1 over denominator 2 end fraction g left parenthesis t to the power of 2 end exponent minus t subscript 1 end subscript superscript 2 end superscript right parenthesis over denominator fraction numerator 1 over denominator 2 end fraction g left parenthesis t to the power of 2 end exponent minus t subscript 2 end subscript superscript 2 end superscript right parenthesis end fraction
    Or negative fraction numerator t subscript 1 end subscript over denominator t subscript 2 end subscript end fraction equals fraction numerator t to the power of 2 end exponent minus t subscript 1 end subscript superscript 2 end superscript over denominator t to the power of 2 end exponent minus t subscript 2 end subscript superscript 2 end superscript end fraction
    By solvingblank t equals square root of t subscript 1 end subscript t subscript 2 end subscript end root

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