question_answer

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\[(\sqrt{3},y).\]The path of the particle makes with the \[x\]-axis an angle of

A) \[30{}^\circ \]                                   

B) \[45{}^\circ \]

C) \[60{}^\circ \]                   

D)        \[0{}^\circ \]

Correct Answer: C

Solution :

Key Idea Slope of the path of the particle gives the measure of angle required. 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                 \[\tan \theta =\]slope of line\[OA\]                          \[=\frac{AB}{OB}=\frac{3}{\sqrt{3}}=\sqrt{3}\] or            \[\theta ={{60}^{o}}\]