The velocity of a particle having magnitude of $10 \mathrm{~ms}^{-1}$ in the direction of $60^{\circ}$ with positive $\mathrm{X}$-axis is

• A

  $5 \hat{i}-5 \sqrt{3} \hat{j}$
• B

  $5 \sqrt{3} \hat{\mathrm{i}}-5 \hat{\mathrm{j}}$
• C

  $5 \sqrt{3} \hat{\mathrm{i}}+5 \hat{\mathrm{j}}$
• Correct answer
  D

  $5 \hat{i}+5 \sqrt{3} \hat{j}$

Solution

$\begin{aligned} & \vec{v}=v \cos \theta \hat{i}+v \sin \theta \hat{j} \\ & =10 \cos 60 \hat{i}+10 \sin 60 \hat{j} \\ & =10 \times \frac{1}{2} \hat{i}+10 \times \frac{\sqrt{3}}{2} \hat{j} \\ & =5 \hat{i}+5 \sqrt{3} \hat{j}\end{aligned}$

Hence, the correct answer is option: 'D'.