Physics-
General
Easy

Question

A body is projected at such angle that the horizontal range is three times the greatest height. The angel of projection is

  1. 42 degree 8 ''/>  
  2. 53 degree 7 ''/>  
  3. 33 degree 7 ''/>  
  4. 25 degree 8 ''/>  

The correct answer is: 53 degree 7 ´


    Let a body be projected at a velocity u at an angle theta with the horizontal. Then horizontal range covered is given by

    R equals fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction blank open parentheses i close parentheses
    and height H is
    H equals 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 blank open parentheses i i close parentheses
    Given, R equals 3 H
    fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction equals 3 cross times 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
    Also, sin2blank theta equals 2 sin invisible function application straight theta cos invisible function application theta
    therefore blank fraction numerator u to the power of 2 end exponent 2 sin invisible function application theta cos invisible function application theta over denominator g end fraction equals 3 cross times 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
    o r blank 2 cos invisible function application theta equals 1.5 sin invisible function application theta
    o r tan invisible function application theta equals fraction numerator 2 over denominator 1.5 end fraction equals 1.33
    o r blank theta equals 53 degree 7 to the power of ´ ´ end exponent
    Hence, angle of projection is 53 degree 7 ´

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