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Straight across or land opposite?

relative-motionvectorsoptimisation

A river is 1 km wide and flows at a steady 3 km/h. You can swim at 5 km/h relative to the water.

  1. How should you aim to cross in the least possible time, and how long does it take? Where do you land?
  2. How should you aim to land directly opposite your starting point, and how long does that take?
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Your velocity is your swimming velocity (relative to the water) plus the current. For the fastest crossing, only the component pointing across the river matters. To land opposite, the upstream component of your swimming must cancel the current.

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