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Q.

A person walks at the rate of 3 km/hr. Rain appears to him in vertical direction at the rate of $3 \sqrt{3}$ km/hr. Find magnitude and direction of true velocity of rain.

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a

6 km/hr, inclined at an angle of $45^{0}$ to the vertical towards the person's motion.

b

3 km/trr, inclined at an angle of $30^{o}$ to the vertical towards the person's motion.

c

6 km/hr, inclined at an angle of $60^{o}$ to the vertical towards the person's motion.

d

6 km/hr, inclined at an angle of $30^{o}$ to the vertical towards the person's motion.

answer is C.

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Detailed Solution

$\vec{v_{\frac{r}{m}}} = \vec{v_{r}} - \vec{v_{m}}$

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$\vec{v_{r}} = \vec{v_{r}} - \vec{v_{m}}$

$\tan θ = \frac{3}{3 \sqrt{3}} = \frac{1}{\sqrt{3}} \Rightarrow θ = 30^{0}$

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A person walks at the rate of 3 km/hr. Rain appears to him in vertical direction at the rate of 33 km/hr. Find magnitude and direction of true velocity of rain.