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## Homework Statement

**A river of width 4 km flows at 5 km/h. A swimmer whose speed relative to water is 4 km/h, starts swimming from a point A on a bank. What minimum distance will the swimmer have to walk on the other bank to reach point B directly opposite to A?**

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## Homework Equations

**Vba = Vb - Va is the equation for relative velocity**

## The Attempt at a Solution

**Let Vwg be absolute velocity of river (vector), Vsw be relative velocity of swimmer wrt river (vector) and Vsg be absolute velocity of swimmer wrt ground (vector). Now I know that**

Vsg = Vwg + Vsw

but what angles do the vectors make? I would have supposed that the swimmer makes his strokes at right angles to the river current and therefore the vectors form a right triangle with Vsw perpendicular to Vwg and therefore Vsg will be the hypotenuse, but the answer for the value of Vsq is 3 and this would not follow Pythagoras theorem. What angles do the vectors make then? How do I do this?

Vsg = Vwg + Vsw

but what angles do the vectors make? I would have supposed that the swimmer makes his strokes at right angles to the river current and therefore the vectors form a right triangle with Vsw perpendicular to Vwg and therefore Vsg will be the hypotenuse, but the answer for the value of Vsq is 3 and this would not follow Pythagoras theorem. What angles do the vectors make then? How do I do this?

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