A particle starting from the origin $(0,0)$ moves in a straight line in the $(x, y)$ plane. Its coordinates at a later time are $(\sqrt{3}, 3)$. The path of the particle makes with the $x$-axis an angle of

• A

  $30^{\circ}$
• B

  $45^{\circ}$
• Correct answer
  C

  $60^{\circ}$
• D

  $0^{\circ}$

Solution

Draw the situation as shown. OA represents the path of the particle starting from origin $O(0,0)$ Draw a perpendicular from point $A$ to x-axis. Let path of the particle makes an angle $\theta$ with the x -axis, then $\begin{aligned} \tan \theta & =\text { slope of line } O A \\ & =\frac{A B}{O B}=\frac{3}{\sqrt{3}}=\sqrt{3} \\ \text { or } \quad \theta & =60^{\circ}\end{aligned}$

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