Question

A car drives 215km east and then 45km north. What is the magnitude of the cars displacement? Round you answer to nearest whole number.

Answer 1

Answer: $219.65\ \text{km}$

Explanation:

Given

Car drives 215 km east and then 45 km North

Displacement is East direction is

$\Rightarrow \vec{r_1}=215\hat{i}$

Now, the displacement from that to 45 km North is given by

$\Rightarrow \vec{r_{21}}=45\hat{j}$

Net displacement is $\vec{r_2}$

$\Rightarrow \vec{r_2}=\vec{r_1}+\vec{r_{21}}\\\Rightarrow \vec{r_2}=215\hat{i}+45\hat{j}$

Magnitude of the displacement is

 $\Rightarrow \left | r_{2} \right |=\sqrt{\left ( 215 \right )^2+\left ( 45 \right )^2}\\\Rightarrow \left | r_{2} \right |=\sqrt{48250}\\\Rightarrow \left | r_{2} \right |=219.65\ \text{km}$