Physics-
General
Easy

Question

The horizontal range of a projectile is 4 square root of 3 times its maximum height. Its angle of projection will be

  1. 45 degree  
  2. 60 degree  
  3. 90 degree  
  4. 30 degree  

The correct answer is: 30 degree


    Let u be initial velocity of projection at angle theta with the horizontal. Then, horizontal range,
    R equals fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction
    a n d blank m a x i m u m blank h e i g h t blank H equals fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator 2 g end fraction
    G i v e n comma blank R equals 4 square root of 3 H
    therefore blank fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction equals 4 square root of 3 bullet fraction numerator u to the power of 2 end exponent s i n to the power of 2 end exponent theta over denominator 2 g end fraction
    therefore blank 2 sin invisible function application theta cos invisible function application theta equals 2 square root of 3 s i n to the power of 2 end exponent theta
    o r blank fraction numerator cos invisible function application theta over denominator sin invisible function application theta end fraction equals square root of 3
    o r cot invisible function application theta equals square root of 3 equals cot invisible function application 30 degree

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