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Question

A man walks at the rate of 3 km/hr. Rain appears to him falling in vertical direction at the rate of 33 km/hr. Which of the following options is correct regarding the actual velocity of rain?

A
6 km/hr, inclined at an angle of 30 to the vertical towards the man's motion.
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B
3 km/hr, inclined at an angle of 30 to the vertical towards the man's motion.
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C
6 km/hr, inclined at an angle of 45 to the vertical towards the man's motion.
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D
6 km/hr, inclined at an angle of 60 to the vertical towards the man's motion.
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Solution

The correct option is A 6 km/hr, inclined at an angle of 30 to the vertical towards the man's motion.
Let vr be the actual velocity of rain.
Speed of rain w.r.t man, vr/m=33 km/hr
Speed of man w.r.t ground, vm=3 km/hr

vr/m=vrvm
vr=vr/m+vm
|vr|=v2r/m+v2m
=(3)2+(33)2=6 km/hr
tanθ=333=13θ=30

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