$A$ river is flowing from east to west at a speed of $5\, m/min$. $A$ man on the south bank of the river,capable of swimming $10\, m/min$ in still water,wants to swim across the river in the shortest time. He should swim:

  • A
    Due north
  • B
    Due north-east
  • C
    Due north-east with double the speed of the river
  • D
    None of these

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$A$ man can swim with velocity $v$ relative to water. He has to cross a river of width $d$ flowing with a velocity $u$ $(u > v)$. The distance through which he is carried downstream by the river is $x$. Which of the following statements is correct?

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