(A) Given, speed of rain in vertical direction, $v_r = 30 \,m/s$.Speed of the man, $v_m = 10 \,m/s$ (towards West).The relative velocity of rain with

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(A) Given, speed of rain in vertical direction, $v_r = 30 \,m/s$.Speed of the man, $v_m = 10 \,m/s$ (towards West).The relative velocity of rain with respect to the man is $\vec{v}_{rm} = \vec{v}_r - \vec{v}_m$.Since the man is moving towards the West, the relative velocity vector $\vec{v}_{rm}$ will be directed towards the West relative to the vertical.Let $\theta$ be the angle with the vertical.From the vector triangle, $\tan \theta = \frac{v_m}{v_r} = \frac{10}{30} = \frac{1}{3}$.Therefore, $\theta = \tan^{-1}(1/3)$ towards the West direction.

Class 11 Physics 3-2.Motion in Plane Relative Velocity (river boat, rain, wind)

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Rain is falling vertically with a speed of $30 \,m/s$. A man rides a bicycle with a speed of $10 \,m/s$ from East to West direction. At what angle with the vertical does he see the rain falling?

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A
$\tan^{-1}(1/3)$ towards West
B
$\tan^{-1}(3)$ towards West
C
$\tan^{-1}(1/3)$ towards East
D
$\tan^{-1}(3)$ towards East

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3-2.Motion in Plane

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Relative Velocity (river boat, rain, wind)

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Rain is falling vertically with a speed of $30 \,m/s$. A man rides a bicycle with a speed of $10 \,m/s$ from East to West direction. At what angle with the vertical does he see the rain falling?

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