Suppose you first walk 25.1 m in a direction 15.4º west of north and then 38.8 m in a direction 23.1º south of west. How far are you from your starting point?

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Answer :

Vespertilio Vespertilio · Answer 1 · 2024-02-24T20:54:59-05:00

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.