Question

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?

Answer 1

43.3 m

Step-by-step 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

`\overrightarrow{d_(1)}=25.1\left ( -Sin15.4\widehat{i}+Cos15.4\widehat{j} \right )=-6.67\widehat{i}+24.2\widehat{j}`

`\overrightarrow{d_(2)}=38.8\left ( -Cos23.1\widehat{i}-Sin23.1\widehat{j} \right )=-35.69\widehat{i}-15.22\widehat{j}`

The resultant displacement is given by

`\overrightarrow{d}=\overrightarrow{d_(1)}+\overrightarrow{d_(2)}`

`\overrightarrow{d}}=\left ( -6.67-35.69 \right )\widehat{i}+\left ( 24.2-15.22 \right )\widehat{j}`

`\overrightarrow{d}}=\left ( -42.36 \right )\widehat{i}+\left ( 8.98 \right )\widehat{j}`

The magnitude of the resultant displacement is given by

`d=\sqrt{8.98^(2)+\left ( -42.36 \right )^(2)}=43.3 m`

Thus, you are 43.3 m far from your starting point.