Question

ornithologists have determined that some species o fly over water than land because air generally rises over land and falls over water during the day. A bird with these tendencies is released from an island that is 3 km from the nearest point B on the shoreline, flies to a point C on the shoreline, and then flies along the shoreline to its nesting area D. Assume that the bird instinctively chooses a path that will minimize its energy expenditure. Points B and D are 16 km apart. (Round your answers to two decimal places.) f birds more energy is required to avold rlights over Targe bodles or Water during daylight hours. It IS belleved tha island nest a) In general ıf it takes 1 1 times as much energy to fly over water as land, to what point С should the bird fly in order to minimize the total energy expended in returning to its nesting area? km from B (b) Let W and L denote the energy (in joules) per kilometer flown over water and land, respectively. Assuming the bird's energy expenditure is minimized, determine a function for the ratio W/L in terms of x, the distance from B to C. (c) What should the value of W/L be in order for the bird to fly directly to its nesting area D? (d) If the ornithologists observe that birds of a certain species reach the shore at a point 3 km from B, how many times more energy does it take a bird to fly over water than land?

Answer 1

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