Question

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. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. $0^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

Let, $\theta$ be the angle which the particle makes with an x-axis.

From the given figure:
$tan\theta =\frac{y}{x}=\frac{3}{\sqrt{3}}=\sqrt{3}\Rightarrow \theta =ta{n}^{-1}\sqrt{3}={60}^{\circ }$.
Hence, the correct answer is option (b).