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Question

Galileo writes that for angles of projection of a projectile at angles left parenthesis 45 plus theta right parenthesis and open parentheses 45 minus theta close parentheses comma blankthe horizontal ranges described by the projectile are in the ratio of left parenthesisif theta less or equal than 45 right parenthesis

  1. 2 blank colon 1  
  2. 1 blank colon 2  
  3. 1 blank colon 1  
  4. 2 blank colon 3  

The correct answer is: 1 blank colon 1


    For angle open parentheses 45 degree minus theta close parentheses comma R equals fraction numerator u to the power of 2 end exponent sin invisible function application open parentheses 90 degree minus 2 theta close parentheses over denominator g end fraction equals fraction numerator u to the power of 2 end exponent cos invisible function application 2 theta over denominator g end fraction
    For angleopen parentheses 45 degree plus theta close parentheses comma blank R equals fraction numerator u to the power of 2 end exponent sin invisible function application open parentheses 90 degree plus 2 theta close parentheses over denominator g end fraction equals fraction numerator u to the power of 2 end exponent cos invisible function application 2 theta over denominator g end fraction

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