What are (a) the x component and (b) the y component of a vector in the xy plane if its direction is 259° counterclockwise from the positiv

Question

What are (a) the x component and (b) the y component of a vector in the xy plane if its direction is 259° counterclockwise from the positive direction of the x axis and its magnitude is 5.4 m?

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Khải Quang 5 years 2021-09-02T13:38:11+00:00 2 Answers 21 views 0

Answers ( )

  1. Verity
    0
    2021-09-02T13:39:44+00:00
    Reply

    Answer:

    |Ax| =1.03 m  (directed towards negative x-axis)

    |Ay|= 5.30 (directed towards negative y-axis)

    Explanation:

    Let A is a vector = 5.4 m

    θ = 259°

    to Find Ax, Ay

    Sol:

    according the condition it lies in 3rd quadrant

    we know that Horizontal Component Ax = A cos θ

    Ax = 5.4 Cos 259°

    Ax = – 1.03 m

    |Ax| =1.03 m  (directed towards negative x-axis)

    Now Ay = A sin θ

    Ay = 5.4 Sin 259°

    Ay = -5.30

    |Ay|= 5.30 (directed towards negative y-axis)

  2. danthu
    0
    2021-09-02T13:40:00+00:00
    Reply

    Answer:

    (a) -1.030m

    (b) -5.301m

    Explanation:

    Given a vector F in the xy plane, of magnitude F and in a direction θ counterclockwise from the positive direction of the x-axis;

    The x-component (F_{X}) of vector F is given by;

    F_{X} = F cos θ    ———————(i)

    And;

    The y-component (F_{Y}) of vector F is given by;

    F_{Y} = F sin θ            ———————–(ii)

    Now to the question;

    Let the vector be A

    Therefore;

    The magnitude of vector A is A = 5.4m

    The direction θ of A counterclockwise from the positive direction of the x-axis = 259°

    (a) The x-component (A_{X}) of the vector A is therefore given by;

    A_{X} = A cos θ       ————————(iii)

    Substitute the values of θ and A into equation (iii) as follows;

    A_{X} = 5.4 cos 259°

    A_{X} = 5.4 x (-0.1908)

    A_{X} = -1.030

    Therefore, the x-component of the vector is -1.030m

    (b) The y-component (A_{Y}) of the vector A is therefore given by;

    A_{Y} = A sin θ       ————————(iv)

    Substitute the values of θ and A into equation (iv) as follows;

    A_{Y} = 5.4 sin 259°

    A_{Y} = 5.4 x (-0.9816)

    A_{Y} = -5.301m

    Therefore, the y-component of the vector is -5.301m

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