Physics-
General
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Question

In a two dimensional motion of a particle, the particle moves from point A, position vector stack r with rightwards arrow on top subscript 1 end subscript. If the magnitudes of these vectors are respectively, r subscript 1 end subscript=3 and r subscript 2 end subscript equals 4 and the angles they make with the x-axis are theta subscript 1 end subscript equals 75 degree and 15degree, respectively, then find the magnitude of the displacement vector

  1. 15    
  2. square root of 13    
  3. 17    
  4. square root of 15    

The correct answer is: 17


    Displacement equals A B
    angle between stack r subscript 1 end subscript with rightwards arrow on top and stack r subscript 2 end subscript with rightwards arrow on top
    theta equals 75 degree minus 15 degree equals 60 degree
    From figure
    A B to the power of 2 end exponent equals r subscript 1 end subscript superscript 2 end superscript plus r subscript 2 end subscript superscript 2 end superscript minus 2 r subscript 1 end subscript r subscript 2 end subscript c o s theta
    equals 3 to the power of 2 end exponent plus 4 to the power of 2 end exponent minus 2 cross times 3 cross times 4 cos60 degree
    equals 13
    A B equals square root of 13

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