Question

4.14*. A fisherman lives on the shore of a bay forming a wedge with angle ? in a house located at point A (Fig. 119). The distance B. Fig. 119 from point A to the nearest point C of the bay is e, and the distance from point D to roint A is l. A friend of the fisherman lives across the bay in a house located at B. Pcint Bis symmetric (relative to the av) to point A. The fisherman has a boat. Determine the minimum time t required for the fisherman to get to his friend from the house provided that he can move along the shore at a velocity v and row the boat point at half that velocity (n 2). 15 Tho i

Answer 1

"The problem is analogous to the optical problem in which the reflection of a plane wave in a prism is analyzed. According to the laws of geometrical optics, the light ray propagating from point A to point b (Fig). takes the shortest time in comparison with all other paths. The fisherman must move along the path of a ""light ray"" , i.e . must approach point E of the bay at an angle gamma, cross the bay in a boat at right angles to the bisector of the angle alpha, and then move along the shore in the direction of point B. Fig The angle gamma can be determined from snell's law (n = 2): sin gamma = n sin alpha/2. The distance alpha is a = h tan gamma = h n sin (alpha/2)/ squareroot 1 - n^2 sin^2 (alpha/2). The distance b can be determined from the equation a + b "

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