Answer:
Explanation:
Given
First car travels [tex]225\ km[/tex] west so its position vector is given by
[tex]\vec{r_1}=-225\hat{i}[/tex]
then it travels in south-west direction for [tex]98\ km[/tex]
[tex]\vec{r_{21}}=98(-\cos (45)\hat{i}-\sin (45)\hat{j})[/tex]
so position vector of [tex]\vec{r_2}[/tex] is
[tex]=\vec{r_{21}}+\vec{r_1}[/tex]
[tex]=98(-\cos (45)\hat{i}-\sin (45)\hat{j})-225\hat{i}[/tex]
[tex]=-(69.29+225)\hat{i}-69.29\hat{j}[/tex]
[tex]=-294.29\hat{i}-69.29\hat{j}[/tex]
Magnitude of displacement is given by
[tex]|\vec{r_2}|=\sqrt{294.29^2+69.29^2}[/tex]
[tex]|\vec{r_2}|=302.34\ km[/tex]
