Question

Please solve both. Same problem but one is looking for vector R and the other vector D.

2. A vector A has a magnitude of 60.0 m and points in a direction 28.0P above the negative x-axis. A second vector, B, has a magnitude of 840 m and points in a direction 58.0° below the positive x-axis. Using the component method, find the magnitude of the vector R-A+B. 3. A vector A has a magnitude of 60.0 m and points in a direction 28.0° above the negative x-axis. A second vector. B. has a magnitude of 84.0 m and points in a direction 58.0° below the positive x-axis. Using the component method, find the magnitude of the vector D- A-B

Answer 1

$\vec{A}=60m\ at\ 28^{\circ} \ above\ -x \ axis$

X component is negative and y component is positive

$\vec{A}=-A_{x}i+A_{y}j$

$\vec{A}=-Acos28i+Asin28j$

$\vec{A}=-60cos28i+60sin28j$

${\color{Red} \vec{A}=(-52.98i+28.17j)m}$

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$\vec{B}=84m\ at\ 58^{\circ} \ below\ x \ axis$

X component is positive and y component is negative

$\vec{B}=B_{x}i-B_{y}j$

$\vec{B}=Bcos58i-Bsin58j$

$\vec{B}=84cos58i-84sin58j$

${\color{Red} \vec{B}=(44.51i-71.24j)m}$

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$\vec{R}=\vec{A}+\vec{B}$

$\vec{R}=(-52.98i+28.17j)+(44.51i-71.24j)$

$\vec{R}=(-8.47i-42.07j)m$

$R=\sqrt{(-8.47)^{2}+(-42.07)^{2}}$

ANSWER: ${\color{Red} R=42.91m}$

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$\vec{D}=\vec{A}-\vec{B}$

$\vec{D}=(-52.98i+28.17j)-(44.51i-71.24j)$

$\vec{D}=(-97.49i+99.41j)m$

$D=\sqrt{(-97.49)^{2}+(99.41)^{2}}$

ANSWER: ${\color{Red} D=139.24m}$

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