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Question

A stone is dropped from a height h. Simultaneously, another stone is thrown up from the ground which reaches a height 4 blank h. The two stones cross other after time

  1. square root of fraction numerator h over denominator 8 g end fraction end root  
  2. square root of 8 g h end root  
  3. square root of 2 g h end root  
  4. square root of fraction numerator h over denominator 2 g end fraction end root  

The correct answer is: square root of fraction numerator h over denominator 8 g end fraction end root


    For first stone u equals 0 and
    For second stone fraction numerator u to the power of 2 end exponent over denominator 2 g end fraction 4 h rightwards double arrow u to the power of 2 end exponent equals 8 g h
    therefore u equals square root of 8 g h end root
    Now, h subscript 1 end subscript equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent
    h subscript 2 end subscript equals square root of 8 g h t minus fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent end root

    u equals square root of 8 g h end root
    Where,t equalstime cross each other
    therefore h subscript 1 end subscript plus h subscript 2 end subscript equals h
    rightwards double arrow fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent plus square root of 8 g h t end root minus fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent equals h rightwards double arrow t equals fraction numerator h over denominator square root of 8 g h end root end fraction=square root of table row cell fraction numerator h over denominator 8 g end fraction end cell row cell end cell end table end root

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