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 and points P and T are at a distance of d.

Question: If the man rows with a speed of v_r and walks with a speed of v_w , 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 t_der 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.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)