A paricle starting from the origin (0,0) moves in a straight line in (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

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `0^(@)`

Explanation

To find the angle θ that the path of the particle makes with the x-axis, we can use the coordinates of the point where the particle is located, which are (√3, 3).

### Step-by-Step Solution:

1. **Identify the Coordinates**: The particle moves from the origin (0, 0) to the point (√3, 3).

2. **Use the Tangent Function**: The angle θ that the line makes with the x-axis can be determined using the tangent function:
\[ \tan(\theta) = \frac{y}{x} \]
where \(y\) is the vertical coordinate and \(x\) is the horizontal coordinate.

3. **Substitute the Coordinates**: In our case, \(x = \sqrt{3}\) and \(y = 3\). Thus, we can substitute these values into the tangent function:
\[ \tan(\theta) = \frac{3}{\sqrt{3}} \]

4. **Simplify the Expression**: Simplifying the fraction gives:
\[ \tan(\theta) = \frac{3}{\sqrt{3}} = \sqrt{3} \]

5. **Find the Angle**: The angle whose tangent is \(\sqrt{3}\) is:
\[ \theta = 60^\circ \]

### Final Answer:
The angle θ that the path of the particle makes with the x-axis is \(60^\circ\).

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