Question

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

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

Answer 1

The correct option is C ${60}^0$

Particle starts moving from $(0,0)$ and goes till $(\sqrt{3},3)$.

So total displacement along $x$ axis is $\sqrt{3}$ unites and along $y$ axis is $3$ units.

We know that:

$\Rightarrow tan\left(\theta \right)=\frac{y}{x}$

$\Rightarrow tan\left(\theta \right)=\frac{3}{\sqrt{3}}$

$\Rightarrow tan\left(\theta \right)=\sqrt{3}$

$\Rightarrow \theta =\frac{\pi }{3}={60}^0$