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Question

A body thrown vertically up to reach its maximum height in t second. The total time from the time of projection to reach a point at half of its maximum height while returning (in secon(d) is

  1. square root of 2 blank t  
  2. open parentheses 1 plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses t  
  3. fraction numerator 3 t over denominator 2 end fraction  
  4. fraction numerator t over denominator square root of 2 end fraction  

The correct answer is: open parentheses 1 plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses t


    The ball is thrown vertically upwards, then according to equation of motion.
    open parentheses 0 close parentheses to the power of 2 end exponent minus u to the power of 2 end exponent equals negative 2 g h blank open parentheses i close parentheses
    And blank 0 equals u minus g t blank open parentheses i i close parentheses
    From Eqs. (i) and (ii),
    h equals fraction numerator g t to the power of 2 end exponent over denominator 2 end fraction
    When the ball is falling downwards after reaching the maximum height
    s equals u t to the power of ´ end exponent plus fraction numerator 1 over denominator 2 end fraction g open parentheses t to the power of ´ end exponent close parentheses to the power of 2 end exponent
    fraction numerator h over denominator 2 end fraction equals open parentheses 0 close parentheses t to the power of ´ end exponent plus fraction numerator 1 over denominator 2 end fraction g open parentheses t to the power of ´ end exponent close parentheses to the power of 2 end exponent
    rightwards double arrow blank t to the power of ´ end exponent equals square root of fraction numerator h over denominator g end fraction end root
    t to the power of ´ end exponent equals fraction numerator t over denominator square root of 2 end fraction
    Hence, the total time from the time of projection of reach a point at half of its maximum height while returning equals t plus t ´
    equals t plus fraction numerator t over denominator square root of 2 end fraction equals open parentheses 1 plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses t

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