Physics-
General
Easy

Question

A ball thrown upward from the top of a tower with speed v reaches the ground in t subscript 1 end subscript second. If this ball is thrown downward from the top of he same tower with speed v it reaches the ground in t subscript 2 end subscript second. In what time the ball shall reach the ground if it is allowed to falls freely under gravity from the top of the tower?

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

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


    h equals negative v t subscript 1 end subscript plus fraction numerator 1 over denominator 2 end fraction g t subscript 1 end subscript superscript 2 end superscript or fraction numerator h over denominator t subscript 1 end subscript end fraction equals negative v plus fraction numerator 1 over denominator 2 end fraction g t subscript 1 end subscript(i)
    h equals v t subscript 2 end subscript plus fraction numerator 1 over denominator 2 end fraction g t subscript 1 end subscript superscript 2 end superscript or negative fraction numerator h over denominator t subscript 2 end subscript end fraction equals negative v plus fraction numerator 1 over denominator 2 end fraction g t subscript 2 end subscript(ii)
    therefore blank fraction numerator h over denominator t subscript 1 end subscript end fraction plus fraction numerator h over denominator t subscript 2 end subscript end fraction equals fraction numerator 1 over denominator 2 end fraction g left parenthesis t subscript 1 end subscript plus t subscript 2 end subscript right parenthesis
    or h equals fraction numerator 1 over denominator 2 end fraction g t subscript 1 end subscript t subscript 2 end subscript
    For falls under gravity from the top of the tower
    h equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent
    therefore blank fraction numerator 1 over denominator 2 end fraction g t subscript 1 end subscript t subscript 2 end subscript equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent rightwards double arrow t equals square root of t subscript 1 end subscript t subscript 2 end subscript end root

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