A drifting boat

A river is flowing at a uniform velocity of \(v = 10 \text{ m/s}\). As shown in the diagram, \(P\), \(Q\), and \(R\) are three points on a line perpendicular to the river such that \(PQ =QR = 100 \text{ m} \).

A boat starts from point \(P\) and moves at a constant speed of \(v = 10 \text{ m/s} \) relative to the river. It moves in such a way that the direction of its resultant velocity is always perpendicular to the line joining the boat and point \(R\).

If the boat drifts \(a\) meters and takes \(b\) seconds to land on point \(S,\) submit your answer as \(a + b\) to 3 decimal places.

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