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A man sinms across a river with speed of...

A man sinms across a river with speed of `V_(m)` perpendicular to the flow direction of river. If the water flows with a speed ` V_(w)` with what resullant velocity does the man cross the river ?

Text Solution

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The directions of `barv_(m)` and `barv_(w)` are shown in the figure. Using the triangle method the resultant velocity is given by third side of `DeltaAOC` taken in opposite order .

`bar(AC)=bar(AO)+bar(OC)`
` |bar(AC)|=sqrt(A0O^(2)+OC^(2))" " ` [ Using Pythagoras theorem ]
`= sqrt(v_(m)^(2)+v_(w)^(2))`
The direction `theta ` that the resultant makes with the `barv_(m)` is
`tan theta =(|barv_(w)|)/(|barv_(m)|)`
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