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Physics · MOTION IN A PLANE
हिन्दीA position vector \( \mathbf{r} \) in the x-y plane has a magnitude of 10 m and makes an angle of \( 30^\circ \) with the positive y-axis towards the positive x-axis. What are its rectangular components \( r_x \) and \( r_y \)?
Correct answer · Option 2
\( r_x = 5\text{ m} \), \( r_y = 5\sqrt{3}\text{ m} \)
Explanation
The angle with the x-axis is \( 90^\circ - 30^\circ = 60^\circ \). Thus \( r_x = r\cos 60^\circ = 10 \times 0.5 = 5\text{ m} \) and \( r_y = r\sin 60^\circ = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}\text{ m} \).
