Maths-
General
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Question

The angular elevation of an enemy's position on a hill h feet high is beta. Show that is order to shell if the initial velocity of the projectile must not be less than

  1. left square bracket g h left parenthesis 1 plus sin invisible function application beta right parenthesis right square bracket to the power of 1 divided by 2 end exponent    
  2. left square bracket g h left parenthesis 1 minus sin invisible function application beta right parenthesis right square bracket to the power of 1 divided by 2 end exponent    
  3. left square bracket g h left parenthesis 1 plus text cosec  end text beta right parenthesis right square bracket to the power of fraction numerator 1 over denominator 2 end fraction end exponent    
  4. left square bracket g h left parenthesis 1 minus cot invisible function application sec invisible function application beta right parenthesis right square bracket to the power of 1 half end exponent    

The correct answer is: left square bracket g h left parenthesis 1 plus text cosec  end text beta right parenthesis right square bracket to the power of fraction numerator 1 over denominator 2 end fraction end exponent


    Let u be the velocity of projection. The coordinates of enemy’s position with reference to horizontal and vertical lines through the point of projection as the coordinates axes are left parenthesis h cot invisible function application beta comma h right parenthesis For the projection to hit at left parenthesis h cot invisible function application beta comma h right parenthesis we must have.
    u to the power of 2 end exponent greater or equal than g open square brackets h plus square root of h to the power of 2 end exponent cot to the power of 2 end exponent invisible function application beta plus h to the power of 2 end exponent end root close square brackets
    Þ u to the power of 2 end exponent greater or equal than g left square bracket h plus h c o s e c beta right square bracket Þ u greater or equal than square root of g h left parenthesis 1 plus cos invisible function application rightwards arrow over short leftwards arrow e c beta right parenthesis end root.

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