During daylight hours, some birds fly more slowly over water than over land beca

Question

During daylight hours, some birds fly more slowly over water than over land because some of their energy is expended in overcoming the downdrafts of air over open bodies of water. Suppose a bird that flies at a constant speed of 2 mph over water and 4 mph over land starts its journey at the point E on an island and ends at its nest Non the shore of the mainland, as shown in the figure below. Find the location of the point P that allows the bird to complete its journey in the minimum time (solve for x). (Round your answer to two decimal places.)

Explanation / Answer

t=sqrt(x^2+9)/2+(12-x)/4

dt/dx=0.5x/sqrt(x^2+9)-1/4=0

so x=1.732 mi

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