A helicopter goes straight up 500m from a landing pad. It then goes north 20m. Then it goes down 452m. a) What is the displacement of the he

Question

A helicopter goes straight up 500m from a landing pad. It then goes north 20m. Then it goes down 452m. a) What is the displacement of the helicopter?
Express as components of a vector.
x-component_____________________
y-component_____________________

b) What is the displacement of the helicopter? Express as a vector (magnitude and direction).

Answer_____________________

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Latifah 1 year 2021-08-06T15:31:04+00:00 1 Answers 5 views 0

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    2021-08-06T15:32:42+00:00

    Answer:

    a

      x-component             [tex]20 \ m[/tex]

    y-component     [tex]500 – 452 = 48 \ m[/tex]

    b

     Magnitude [tex]d = 52 \ m[/tex]

    direction is  [tex]\theta = 67.4^o[/tex]

    Explanation:

    From the question we are told that

       The first  vertical distance is  [tex]y_1 = 500 \ m[/tex]

        The  first horizontal distance  is  [tex]x = 20 \ m[/tex]

        The  second vertical distance is  [tex]y_2 = 452 \ m[/tex]

    Generally the displacement is  

    x-component             [tex]20 \ m[/tex]

    y-component     [tex]500 – 452 = 48 \ m[/tex]

    Generally the helicopters displacement is mathematically evaluated as  

           [tex]d = \sqrt{ x- component ^2 + y- component ^2 }[/tex]

          [tex]d = \sqrt{ 20t ^2 + 48 ^2 }[/tex]

          [tex]d = 52 \ m[/tex]

    The  direction is the angle the displacement of the helicopter makes with the horizontal which is mathematically evaluated as

             [tex]\theta = tan ^{-1}[ \frac{48}{20}][/tex]

    =>       [tex]\theta = tan ^{-1}[ 2.4 ][/tex]

    =>      [tex]\theta = 67.4^o[/tex]

       

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