Question

Vector A has magnitude 8.00 m and is in the xy-plane at an angle of 127∘ counterclockwise from the +x-axis ( 37∘ past the +y-axis). The sum A+B is in the −y-direction and has magnitude 12.0 m. What is the magnitude of vector B ? Express your answer with the appropriate unit

Answer 1

H,

Explanation:

`\overrightarrow{OA}=8*(cos(-127^o)*\vec{i}+sin(-127^o)*\vec{j})\\\\\overrightarrow{OS}=\overrightarrow{OA}+\overrightarrow{OB}\\=12*(cos(90^o)*\vec{i}+sin(90^o)*\vec{j})\\\\\overrightarrow{OB}=12*(cos(90^o)*\vec{i}+sin(90^o)*\vec{j})-8*(cos(-127^o)*\vec{i}+sin(127^o)*\vec{j})\\\\\overrightarrow{OB}=-8*cos(127^o)*\vec{i}+\vec{j} *(12-8*sin(-127^o))\\\\=-4,81452*\vec{i}+18,38908\vec{j} \\\\||\overrightarrow{OB}||=√((-4,81452)^2+5,61092^2) =19,00889\\\\`

direction B= arctg(18.38908/4.81452)=75,33°