ASK YOUR TEACHER Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water

Question

ASK YOUR TEACHER Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water during the day island 5 km W L B 9 km 1 144 D nest A bird with these tendencies is released from an island that is 5 km from the nearest point B on a straight shoreline flies to a point C on the shoreline and then flies along the shoreline to its nesting area D Points B and D are 9 km apart Assume that the bird instinctively chooses a path that will minimize its energy expenditure Round your answers to two decimal places a In general if it takes 1 2 times as much energy to fly over water as land to what point C should the bird fly in order to minimize the total energy expended in returning to its nesting area 1 5 km from B MY NOTES W L 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 in terms of x the distance from B to C 25 c What should the value of Wbe in order for the bird to fly directly to its nesting area D L X PRACTICE ANOTHER 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 1 144

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