Boat Landing Problem                             Problem DetailsLFS 2007, Created with GeoGebra

Problem setting: A man with a boat at point S at sea wants to get to point Q inland. Point S is distance d1 from the closest point P on the shore, point Q is distance d2 from the closest point T on the shore.The points P and T are at a distance of d from each other.

Question: If the man rows with a speed of vr and walks with a speed of vw , at what point R should he beach the boat in order to get from point S to point Q in the least possible time?

To use: Click and drag any of the slider points. Watch the time function t, the derivative function tder and the point R on the shore change.

Note: Roots are defined as: R - using GeoGebra 'intersection', RN - Newton's method on the derivative, RsRF - regula falsi and RsN - Newton's method on the equivalent (simplified) 4th order polynomial.

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