Question

A is 57.0 m long at a 28 angle with respect to the <x axis. B is 34.0 m long at a 56' angle above the x axis. 1) What is the magnitude of the sum of vectors A and B (Express your answer to two significant figures.) 63 m Submit Your submissions: 63 Computed value: 63Submitted: Wednesday, January 30 at 4:44 PM Feedback: Right answer! 2) what is the angle with the x axis of the sum of vectors A and Bi (Express your answer to two significant figures.) Submit Your submissions: 84 X Computed value: 84 Feedback: Submitted: Wednesday, January 30 at 4:45 PM

Answer 1

$\vec{A}=57m \ at\ 28^{\circ}$

$\vec{A}=A_{x}i&plus;A_{y}j$

$\vec{A}=Acos28i&plus;Asin28j$

$\vec{A}=57cos28i&plus;57sin28j$

${\color{Red} \vec{A}=50.33i&plus;26.76j}$

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$\vec{B}=34m \ at\ 56^{\circ} above -x\ axis$

so x term is negative ,y term is positive

$\vec{B}=B_{x}i&plus;B_{y}j$

$\vec{B}=-Bcos56i&plus;Bsin56j$

$\vec{B}=-34cos56i&plus;34sin56j$

${\color{Red} \vec{B}=-19.01i&plus;28.19j}$

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$\vec{A}&plus;\vec{B}=(50.33i&plus;26.76j)&plus;(-19.01i&plus;28.19j)$

$\vec{A}&plus;\vec{B}=31.32i&plus;54.95j$

Magnitude of $\vec{A}&plus;\vec{B}=\sqrt{31.32^{2}&plus;54.95^{2}}$

Magnitude of $\vec{A}&plus;\vec{B}=63.25m$

ANSWER: ${\color{Red} 63m}$

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Direction of $\vec{A}&plus;\vec{B}=\theta _{\vec{A}&plus;\vec{B}}=tan^{-1}((A&plus;B)_{y}/(A&plus;B)_{x})$

$\theta _{\vec{A}&plus;\vec{B}}=tan^{-1}(54.95/31.32)$

$\theta _{\vec{A}&plus;\vec{B}}=60.32^{\circ}$

ANSWER: ${\color{Red} 60.32^{\circ}}$

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