Question

# A man running along a straight road with uniform velocity →u=uˆi feels that the rain is falling vertically down along −ˆj. If he doubles his speed,he finds that the rain is coming at an angle θ with the vertical. The velocity of the rain with respect to the ground is :

A
uiutanθ^j
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B
uiutanθˆj
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C
utanθuj
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D
utanθiuj
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Solution

## The correct option is B ui−utanθˆjGiven,Velocity of man =→u=u^iLet the velocity of rain =→v=x^i+y^jNow, in first case velocity of rain with respectto man =→VR=→v−→u =(x−u)^i+y^jGiven that It x− component is zero asrain is falling vertically down, and y component is along −ve directionSo, x−u=0⇒x=u∴ velocity of rain =u^i+y^jIn second case when be will doobles his speed velocity of rain with respect to man =→VR⇒→VR=→v−→u=u^i+y^j−2u^i=−u^i+y^jNow this case rain is coming at an angle θ to the vertical∴tanθ=−uy⇒y=−utanθ∴ velocity of rain with respect to ground=→V=x^i+y^j=u^i−ytanθ^j∴ Option B is correct

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