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Question

# A man running on a horizontal road at 8 ms−1 finds rain falling vertically. If he increases his speed to 12 ms−1, he finds that drops make 30∘ angle with the vertical. Find velocity of rain with respect to the road.

A
47 ms1
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B
82 ms1
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C
73 ms1
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D
8.32 ms1
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Solution

## The correct option is D 8.32 ms−1let consider the velocity of rain,→vr=a^i+b^j→vm= velocity of man→vrm= velocity of rain with respect to manCondition (1): →vm=8^i→vrm=0^i+b^j→vr−→vm=b^ja^i+b^j−8^i=b^j(a−8)^i+b^j=b^ja−8=0a=8Condition (2): →vm=12^i→vrm=→vr−→vm→vrm=(a^j+b^j)−12^i→vrm=(a−12)^i+b^jMake 300 angle to the vertical,ba−12=tan300b4−12=1√3b=−4√3So, velocity of rain with respect to the road is,→vr=8^i−4√3^jIt's magnitude, |→vr|=√(8)2+(−4√3)2vr=8.32m/s

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