13 va 202 V Pv 2. Ornithologists have found that the power (in joules per second) consumed by a certain pigeon flying at

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13 Va 202 V Pv 2 Ornithologists Have Found That The Power In Joules Per Second Consumed By A Certain Pigeon Flying At 1 (79.79 KiB) Viewed 20 times

13 va 202 V Pv 2. Ornithologists have found that the power (in joules per second) consumed by a certain pigeon flying at velocity v miles per second is described well by the function P(v) = + Assume that the pigeon can store 7 x 105 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 103) , 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 velocity Va which maximizes D(V) satisfies P. (Va) . Show that Va is obtained graphically as the velocity coordinate of the point where a line through the origin is tangent to the graph of Pav) as shown in the figure below. (d) Find the Va and the maximum distance D(Va). P(Vd) Va Power (dis) Minimum power consumption Maximum distance traveled 10 15 Velocity (ms)