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Physics · MOTION IN A PLANE
हिन्दीRefer to the vector diagram shown in the figure for a person experiencing rain and wind. Rain is falling vertically with a speed \( v_r = 30\text{ m/s} \), and wind is blowing from east to west with a speed \( v_w = 10\sqrt{3}\text{ m/s} \). Calculate the magnitude of the velocity of rain relative to the ground and the angle \( \theta \) with the vertical at which the umbrella should be held to prevent getting wet.
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Correct answer · Option B
\( 20\sqrt{3}\text{ m/s} \), \( 30^\circ \) towards east
Explanation
The resultant speed is \( R = \sqrt{v_r^2 + v_w^2} = \sqrt{30^2 + (10\sqrt{3})^2} = \sqrt{1200} = 20\sqrt{3}\text{ m/s} \). The angle with vertical is given by \( \tan\theta = \frac{v_w}{v_r} = \frac{10\sqrt{3}}{30} = \frac{1}{\sqrt{3}} \implies \theta = 30^\circ \) towards east.
