Homing pigeons will rarely fly over large bodies of water unless forced to do so, presumably because it requires more energy to maintain altitude in flight in the heavy air over cool water. Suppose a pigeon is released from a boat B floating on a lake 5 miles from a point A on the shore and 13 miles from the pigeon’s loft L, as shown in the accompanying figure. Assuming the pigeon requires twice as much energy to fly over water as over land, what path should it follow to minimize the total energy expended in flying from the boat to its loft? Assume the shoreline is straight, and describe your path as a line from B to a point P on the shore followed by a line from P to L.

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B 15 mi A 13 mi P L