Physics-
General
Easy

Question

Two stones are projected with same velocity v at an angle thetaand left parenthesis 90 degree minus theta right parenthesis. If H and H subscript 1 end subscript are greatest heights in the two paths, what is the relation between R comma blank Hand H subscript 1 end subscript?

  1. R equals 4 square root of H H subscript 1 end subscript end root  
  2. R equals square root of H H subscript 1 end subscript end root  
  3. R equals 4 H H subscript 1 end subscript  
  4. None of these  

The correct answer is: R equals 4 square root of H H subscript 1 end subscript end root


    Range of projectile,
    R equals fraction numerator 2 u to the power of 2 end exponent sin to the power of 2 end exponent invisible function application theta over denominator g end fraction(i)
    Height, H equals fraction numerator u to the power of 2 end exponent sin to the power of 2 end exponent invisible function application theta over denominator 2 g end fraction(ii)
    H subscript 1 end subscript equals fraction numerator u to the power of 2 end exponent sin to the power of 2 end exponent left parenthesis 90 degree minus invisible function application theta right parenthesis over denominator 2 g end fraction equals fraction numerator u to the power of 2 end exponent cos to the power of 2 end exponent invisible function application theta over denominator g end fraction(iii)
    Then H H subscript 1 end subscript equals fraction numerator u to the power of 2 end exponent sin to the power of 2 end exponent invisible function application theta cross times u to the power of 2 end exponent cos to the power of 2 end exponent invisible function application theta over denominator 2 g cross times 2 g end fraction(iv)
    From Eq. (i) we get,
    R to the power of 2 end exponent equals fraction numerator 4 u to the power of 2 end exponent sin to the power of 2 end exponent invisible function application theta cross times u to the power of 2 end exponent cos to the power of 2 end exponent invisible function application theta cross times 4 over denominator 2 g cross times 2 g end fraction
    R equals square root of 16 H H subscript 1 end subscript end root [from Eq. (iv)]
    therefore blank R equals 4 square root of H H subscript 1 end subscript end root

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