Chapter 2.5, Problem 116E

Life science: flights of homing pigeons. It is known that homing pigeons tend to avoid flying over water in the daytime, perhaps because downdrafts of air over water make flying difficult. Suppose a homing pigeon is released on an island at point C, which is 3 mi directly out in the water from a point B on shore. Point B is 8 mi downshore from the pigeon’s home loft at point A. Assume that a pigeon flying over water uses energy at a rate 1.28 times the rate over land. Toward what point S downshore from A should the pigeon fly in order to minimize the total energy required to get to the home loft at A? Assume that

S is 4.245 mi downshore from A.

$\begin{array}{l}\text{Total energy}=\left(\text{Energy rate over water}\right)\times \left(\text{Distance over water}\right)+\\ \left(\text{Energy rate over land}\right)\text{×}\left(\text{Distance over land}\right).\end{array}$