ANSWERS
E. Direction = 16°
F. Magnitude = 36 m
EXPLANATION
Given the vectors:
[tex]\begin{gathered} \vec{A}=(30m)\hat{x}+(-8.0m)\hat{y} \\ \vec{B}=(4.5m)\hat{x}+(18m)\hat{y} \end{gathered}[/tex]
We have to find the vector that results from adding these two vectors. To do so, we have to add the components,
[tex]\begin{gathered} \vec{A}+\vec{B}=(30m+4.5m)\hat{x}+(-8.0m+18m)\hat{y} \\ \vec{A}+\vec{B}=(34.5m)\hat{x}+(10m)\hat{y} \end{gathered}[/tex]
Now we have to find the direction and magnitude of the vector.
E. The direction is,
[tex]\theta_{\vec{A}+\vec{B}}=\tan ^{-1}(\frac{y}{x})=\tan ^{-1}(\frac{10}{34.5})\approx16\degree[/tex]
F. The magnitude is the square root of the sum of the squares of the components,
[tex]\vec{|A}+\vec{B}|=\sqrt[]{34.5^2+10^2}=\sqrt[]{1290.25}\approx36m[/tex]
Hence the direction of the sum of vectors A and B is 16° (rounded to the nearest degree) and the magnitude of the resultant is 36 meters (rounded to the nearest meter)
