What is the sum of the following four vectors in (a) unit-vector notation, and as (b) a magnitude and (c) an angle? Positive angles are coun

Question

What is the sum of the following four vectors in (a) unit-vector notation, and as (b) a magnitude and (c) an angle? Positive angles are counterclockwise from the positive direction of the x axis; negative angles are clockwise. = 4.00 m, at 65.0° = 5.00 m, at -235°

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Jezebel 3 years 2021-08-30T19:11:38+00:00 1 Answers 2 views 0

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    2021-08-30T19:13:23+00:00

    Answer:

    The angle will be “124°“. The further explanation is given below.

    Explanation:

    As we know,

    \vec{A}=2m\hat{i}+3m\hat{j}

    \vec{B}=4Cos65^{\circ}\hat{i}+4Sin65^{\circ}\hat{j}

    \vec{C}=-4m\hat{i}-6m\hat{j}

    \vec{D}=5Cos55^{\circ}\hat{-i}+5Sin55^{\circ}\hat{j}

    (a)…

    Let the resultant of \vec{A}, \vec{B}, \vec{C} and \vec{D} will be \vec{R}, then

    ⇒  \vec{R}=\vec{A}+\vec{B}+\vec{C}+\vec{D}

    On putting values, we get

    ⇒      =(2+4Cos65^{\circ}-4+5Cos55^{\circ})\hat{i}+(3+4Sin65^{\circ}-6+5Sin55^{\circ})\hat{j}

    ⇒      =3.17741m(\hat{i})+4.721m(\hat{j})

    (b)…

    On squaring both sides, we get

    ⇒  \left |\vec{R}  \right |=\sqrt{(3.17741)^{2}+(4.721)^{2}}

    ⇒       =5.7 \ m

    (c)…

    Let the resultant angle will be “\theta“,

    ⇒  tan(180-\theta)=\frac{4.721}{3.17741}

    ⇒  180-\theta=56.06

    ⇒  \theta=124^{\circ}

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