Question

A particle moves along a path ABCD as shown in the figure. Then the magnitude of net displacement of the particle from position A to D is

• A. $10m$
• B. $5\sqrt{2}m$
• C. $9m$
• D. $7\sqrt{2}m$

Answer 1

The correct option is D $7\sqrt{2}m$

The resultant displacement is given by
$\overrightarrow{r}=\overrightarrow{r_1}+\overrightarrow{r_2}+\overrightarrow{r_3}$
$\Rightarrow \overrightarrow{r}=3\hat{i}+4\hat{j}+5cos{37}^o\hat{i}+5sin{37}^o\hat{j}$
$\Rightarrow \overrightarrow{r}=3\hat{i}+4\hat{j}+4\hat{i}+3\hat{j}=7\hat{i}+7\hat{j}$
$\therefore$ the magnitude of $\overrightarrow{r}$ is
$\sqrt{7^2+7^2}=7\sqrt{2}m$