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Question: Can a function be found for the bearing of a boat which minimizes its time to cross a river?

Question:Can a function be found for the bearing of a boat which minimizes its time to cross a river?

Earl 930 Maple 2016
optimization
August 22 2017
2

The worksheet below shows a river whose velocity is a function of the distance from its mid point to either bank.

In this worksheet, as an example, a boat of fixed speed crosses the river heading at all times towards its destination which is directly across the river from its starting point. The boat's path is animated.

I presume an experienced boat captain could constantly vary his heading so as to cross in a minimum time.

Can a function for this minimum crossing time heading be found and the worksheet altered to show the minimum time path?

  Rivercrossing.mw

 
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