Q100 / 200 · NEET 2007 · Physics

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:

  • A
    $45^{\circ}$
  • Correct answer
    B
    $60^{\circ}$
  • C
    $0^{\circ}$
  • D
    $30^{\circ}$

Solution

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: \(\begin{aligned} & \Rightarrow \tan (\theta)=\frac{y}{x} \\ & \Rightarrow \tan (\theta)=\frac{3}{\sqrt{3}} \\ & \Rightarrow \tan (\theta)=\sqrt{3} \\ & \Rightarrow \theta=\frac{\pi}{3}=60^{\circ} \end{aligned}\)

Hence, the correct answer is option: 'B'.

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