A particle starting from the origin $(0,0)$ moves in a straight line in the $(x,y)$ plane. Its coordinates at

Question

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 an angle of __________ with the $x$-axis:

Accepted Answer

1. **Identify Coordinates:** The particle moves from the origin $O(0,0)$ to the point $P(\sqrt{3}, 3)$. The displacement vector is $\vec{r} = \sqrt{3}\hat{i} + 3\hat{j}$.
2. **Formula for Direction:** The angle $	heta$ that a vector $\vec{A} = A_x\hat{i} + A_y\hat{j}$ makes with the positive $x$-axis is given by $	an 	heta = \frac{A_y}{A_x}$ .
3. **Substitute Values:** Here, $A_x = x = \sqrt{3}$ and $A_y = y = 3$.
   $$ 	an 	heta = \frac{3}{\sqrt{3}} = \sqrt{3} $$
4. **Calculate Angle:** We know that $	an 60^{\circ} = \sqrt{3}$. Therefore, $	heta = 60^{\circ}$.

Step-by-Step Solution

Practice All PHYSICS Questions