Answer to Question #276972 in Differential Equations for joey

Question

Suppose a pigeon is released form a boat B floating on a lake 5 miles from a point A on the shore and 13 miles from the pigeon’s loft LL. 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 paths as a line from point BB to a point PP on the shore followed by a line from PP to LL. Again, the goal is to find the path pigeon should follow to minimize the total energy expended in flying from the boat to its loft. Draw a picture of this scenario on paper and label it. Use differential Equations and The Techniques of Optimization to solve.