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Question


For a man walking horizontally with speed u, rain appears to hit him vertically down. When he makes his speed 'n' times, rain appears to hit him making an angle θ to the vertical. The original speed of rain is


  1. u1+(n1)2cot2θ

  2. u1+(n1)2tan2θ

  3. u1+(n21)tan2θ

  4. u1+(n21)cot2θ


Solution

The correct option is A

u1+(n1)2cot2θ


VR=VRM(^j)+u^i

V1RM=VRV1m=VRM^j+u^inu^i

V1RM=(n1)u^iVRM^j

tanθ=(n1)uVRmVRm=(n1)u cotθ

VR=u^i(n1)cot θ^j|VR|=u2+(n1)2u2cot2θ

|VR|=u1+(n1)2cot2θ

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