For a swimmer crossing a flowing river, when do I aim upstream and when do I aim straight across?
First decide the target.
First decide the target. For minimum crossing time, use the swimmer's full speed perpendicular to the bank; the river will cause drift. To arrive directly opposite, aim upstream so the upstream component cancels the river velocity; this is possible only if the swimmer is faster than the current. Add swimmer-relative-to-water and water-relative-to-ground as vectors before calculating time or displacement.
Key point
Minimum time and zero drift are different optimisation goals.
Common mistake
using the same direction for both goals.
Memory tip
fastest crossing: straight across; shortest path: cancel the current.
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