Question

What displacement at an angle ${60}^o$ the $x$-axis has an $x$-component of $5m$? $\hat{i}$ and $\hat{j}$ are unit vectors in $x$ and $y$ directions, respectively.

• A. $5\hat{i}$
• B. $5\hat{i}+5\hat{j}$
• C. $5\hat{i}+5\sqrt{3}\hat{j}$
• D. All of the above

Answer 1

The correct option is C $5\hat{i}+5\sqrt{3}\hat{j}$

Let the vector be $\overrightarrow{r}=x\hat{i}+y\hat{j}$

$x=|r|\cos {60}^{\circ }$

$5=|r|\times \frac{1}{2}$

$\Rightarrow |r|=10$ $(x=5)$

$y=|r|\sin {60}^{\circ }$

$\Rightarrow y=5\sqrt{3}$

$\Rightarrow \overrightarrow{r}=5\hat{i}+5\sqrt{3}\hat{j}$