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  4. 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 (√3, 3). The path of the particle makes with the x-axis an angle of

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Q. 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

AIIMSAIIMS 2007

Solution:

Draw the situation as shown. $O A$ 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
image
$\tan \theta=$ slope of line $O A$
$=\frac{A B}{O B}=\frac{3}{\sqrt{3}}=\sqrt{3}$
or $\theta =60^{\circ}$