Physics-
General
Easy

Question

An artillery piece which consistently shoots its shells with the same muzzle speed has a maximum range R. To hit a target which is fraction numerator R over denominator 2 end fraction from the gun and on the same level, the elevation angle of the gun should be

  1. 15 degree  
  2. 45 degree  
  3. 30 degree  
  4. 60 degree  

The correct answer is: 15 degree


    R subscript m a x end subscript equals R equals fraction numerator u to the power of 2 end exponent over denominator g end fraction
    ⟹ u to the power of 2 end exponent equals R g
    N o w comma blank a s blank r a n g e equals fraction numerator u to the power of 2 end exponent s i n 2 theta over denominator g end fraction
    t h e n fraction numerator R over denominator 2 end fraction equals fraction numerator R g s i n 2 theta over denominator g end fraction
    ⟹ s i n 2 theta equals fraction numerator 1 over denominator 2 end fraction equals s i n 30 degree ⟹ theta equals 15 degree

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