Motion In A Plane Ques 20

20. A particle starting from the origin $(0,0)$ moves 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

[2007]

(a) $45^{\circ}$

(b) $60^{\circ}$

(c) $0^{\circ}$

(d) $30^{\circ}$

Show Answer

Answer:

Correct Answer: 20.(b)

Solution:

  1. (b)

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

From figure, $\tan \theta=\frac{3}{\sqrt{3}}=\sqrt{3}$

$\Rightarrow \theta=\tan ^{-1}(\sqrt{3})=60^{\circ}$

If a vector $\vec{R}$ in $X-Y$ plane then its orthogonal vector $R_X=R \cos \theta$ and $R_Y=R \sin \theta$.

$ \text{ And } \frac{R \sin \theta}{R \cos \theta}=\tan \theta=\frac{R_Y}{R_X} $