question_answer

A particle starting from the origin (0, 0) moves in a straight line in die (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:               [AIPMT (S) 2007]

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

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

C) \[{{60}^{o}}\]

D) \[{{0}^{o}}\]

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 \[O(0,\text{ }0)\]. Draw a perpendicular from point A to x-axis. Let path of 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         \[\theta ={{60}^{o}}\]