Answer: [tex]219.65\ \text{km}[/tex]
Explanation:
Given
Car drives 215 km east and then 45 km North
Displacement is East direction is
[tex]\Rightarrow \vec{r_1}=215\hat{i}[/tex]
Now, the displacement from that to 45 km North is given by
[tex]\Rightarrow \vec{r_{21}}=45\hat{j}[/tex]
Net displacement is [tex]\vec{r_2}[/tex]
[tex]\Rightarrow \vec{r_2}=\vec{r_1}+\vec{r_{21}}\\\Rightarrow \vec{r_2}=215\hat{i}+45\hat{j}[/tex]
Magnitude of the displacement is
[tex]\Rightarrow \left | r_{2} \right |=\sqrt{\left ( 215 \right )^2+\left ( 45 \right )^2}\\\Rightarrow \left | r_{2} \right |=\sqrt{48250}\\\Rightarrow \left | r_{2} \right |=219.65\ \text{km}[/tex]
