Answer :
Answer:
43.3 m
Explanation:
d1 = 25.1 m in 15.4° west of north
d2 = 38.8 m in 23.1° south of west
Write the displacements in vector form
[tex]\overrightarrow{d_{1}}=25.1\left ( -Sin15.4\widehat{i}+Cos15.4\widehat{j} \right )=-6.67\widehat{i}+24.2\widehat{j}[/tex]
[tex]\overrightarrow{d_{2}}=38.8\left ( -Cos23.1\widehat{i}-Sin23.1\widehat{j} \right )=-35.69\widehat{i}-15.22\widehat{j}[/tex]
The resultant displacement is given by
[tex]\overrightarrow{d}=\overrightarrow{d_{1}}+\overrightarrow{d_{2}}[/tex]
[tex]\overrightarrow{d}}=\left ( -6.67-35.69 \right )\widehat{i}+\left ( 24.2-15.22 \right )\widehat{j}[/tex]
[tex]\overrightarrow{d}}=\left ( -42.36 \right )\widehat{i}+\left ( 8.98 \right )\widehat{j}[/tex]
The magnitude of the resultant displacement is given by
[tex]d=\sqrt{8.98^{2}+\left ( -42.36 \right )^{2}}=43.3 m[/tex]
Thus, you are 43.3 m far from your starting point.
