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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:
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Verified Answer
The correct answer is:
$60^{\circ}$
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:
\(\begin{aligned}
& \Rightarrow \tan (\theta)=\frac{y}{x} \\
& \Rightarrow \tan (\theta)=\frac{3}{\sqrt{3}} \\
& \Rightarrow \tan (\theta)=\sqrt{3} \\
& \Rightarrow \theta=\frac{\pi}{3}=60^{\circ}
\end{aligned}\)
So total displacement along x axis is \(\sqrt{3}\) unites and along y axis is 3 units.
We know that:
\(\begin{aligned}
& \Rightarrow \tan (\theta)=\frac{y}{x} \\
& \Rightarrow \tan (\theta)=\frac{3}{\sqrt{3}} \\
& \Rightarrow \tan (\theta)=\sqrt{3} \\
& \Rightarrow \theta=\frac{\pi}{3}=60^{\circ}
\end{aligned}\)
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