With detailed solution

2. Bird Migration Omithologists have found that the power (in joules per second) consumed by a certain pigeon flying at velocity v m/s is described well by the function P(v) = 13 Assume that the pigeon can store 7 x 10' J of usable energy as body fat. (a) Show that at velocity v, a pigeon can fly a total distance of D(v) = (7 x 10' ) v/ P(v) if it uses all of its stored energy (b) Find the velocity v, that minimizes P(v). (c) Migrating birds are smart enough to fly at the velocity that minimizes distance traveled rather than minimizes power consumption. Show that the velocity V. which maximizes D(v) satisfies P' (va) = P(Va)/Va . Show that v. is obtained graphically as the velocity coordinate of the point where a line through the origin is tangent to the graph of P(v) as shown in the figure below. (d) Find va and the maximum distance D(Va). Power (J/s) Minimum power consumption Maximum distance traveled LA 10 15 Velocity (m/s)