Show your solution and box the answers. Please write clearly. Thank you. Bird Migration Omithologists have found that the power(in joules per second) consumed by acertain pigeon flying at velocity v m/s is described wellby the function13P(v) =202Assume that the pigeon can store 7x 10^5 J of usableenergy as body fat.(a) Show that at velocity v, a pigeon can fly a totaldistance of D(v) = (7 x10^5 ) v/ P(V) if it uses all of itsstored energy.(b) Find the velocity Vp that minimizes P(v), Find Vd andthe maximum distance D(Vd).(c) Migrating birds are smart enough to fly at thevelocity that minimizes distance traveled rather thanminimizes power consumption. Show that the velocityVd which maximizes D(v) satisfies P' (Vd) = P(Vd)/Vd.Show that Vd is obtained graphically as the velocitycoordinate of the point where a line through the originis tangent to the graph of P(v) as shown in the figurebelow.Power () (c) Migrating birds are smart enough to fly at thevelocity that minimizes distance traveled rather thanminimizes power consumption. Show that the velocityVd which maximizes D(v) satisfies P' (Vd) = P(Vd)/Nd.Show that Vd is obtained graphically as the velocity%3Dcoordinate of the point where a line through the originis tangent to the graph of P(v) as shown in the figurebelow.Power ()Minimum powerconsumptionMaximumdistancetraveled10 15Velecity (mis)

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Accepted Answer

Solution:
a). For a time t, the power and energy are related by the following relation. The power…

certain pigeon flying at velocity v m/s is described wel by the function P (v) = + 202 13