Ornithologists have determined that some species of birds tendto avoid flights over large bodies of water during daylight hours.It is believed that more energy is required to fly over water thanland because air generally rises over land and falls over waterduring the day. A bird with these tendencies is released from anisland that is 7 km from the nearest point B on the shoreline,flies to a point C on the shoreline, and then flies along theshoreline to its nesting area D. Assume that the bird instinctivelychooses a path that will minimize its energy expenditure. Points Band D are 17 km apart. (Round your answers to two decimalplaces.)
(a) In general, if it takes 1.1 times as much energy to fly overwater as land, to what point C should the bird fly in order tominimize the total energy expended in returning to its nestingarea? km from B
(b) Let W and L denote the energy (in joules) per kilometerflown over water and land, respectively. Assuming the bird's energyexpenditure is minimized, determine a function for the ratio W/L interms of x, the distance from B to C. W/L =
(c) What should the value of W/L be in order for the bird to flydirectly to its nesting area D? (d) If the ornithologists observethat birds of a certain species reach the shore at a point 6 kmfrom B, how many times more energy does it take a bird to fly overwater than land?
