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

A man swims 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 ` vecv_(m) and vecv_(w)` are shown in the figure. Using the traingle method. The resultant velocity is given by third side of ` triangleAOC` , , taken in opposite order.
`bar(AC)= bar(AO) +bar(OC)`
`|bar(AC)|=sqrt(AO^(2) +OC^(2))` [ using pythogoras therem)
`sqrt(v_(m)^(2)+v_(w)^(2))`
the direction ` theta` the resultant makes with the ` barv_(m)` is ` tan theta = (|barv_(w)|)/(|barv_(m)|)`
` Rightarrow theta = tan^(-1) (|barv_(w)|)/(|barv_(m)|)`
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