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

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

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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 13 P(v) = 202 Assume that the pigeon can store 7x 10^5 J of usable energy as body fat. (a) Show that at velocity v, a pigeon can fly a total distance of D(v) = (7 x10^5 ) v/ P(V) if it uses all of its stored energy. (b) Find the velocity Vp that minimizes P(v), Find Vd and the maximum distance D(Vd). (c) Migrating birds are smart enough to fly at the velocity that minimizes distance traveled rather than minimizes power consumption. Show that the velocity Vd which maximizes D(v) satisfies P' (Vd) = P(Vd)/Vd. Show that Vd 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. Power ()
Transcribed Image Text: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 13 P(v) = 202 Assume that the pigeon can store 7x 10^5 J of usable energy as body fat. (a) Show that at velocity v, a pigeon can fly a total distance of D(v) = (7 x10^5 ) v/ P(V) if it uses all of its stored energy. (b) Find the velocity Vp that minimizes P(v), Find Vd and the maximum distance D(Vd). (c) Migrating birds are smart enough to fly at the velocity that minimizes distance traveled rather than minimizes power consumption. Show that the velocity Vd which maximizes D(v) satisfies P' (Vd) = P(Vd)/Vd. Show that Vd 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. Power ()
(c) Migrating birds are smart enough to fly at the velocity that minimizes distance traveled rather than minimizes power consumption. Show that the velocity Vd which maximizes D(v) satisfies P' (Vd) = P(Vd)/Nd. Show that Vd is obtained graphically as the velocity %3D coordinate of the point where a line through the origin is tangent to the graph of P(v) as shown in the figure below. Power () Minimum power consumption Maximum distance traveled 10 15 Velecity (mis)
Transcribed Image Text:(c) Migrating birds are smart enough to fly at the velocity that minimizes distance traveled rather than minimizes power consumption. Show that the velocity Vd which maximizes D(v) satisfies P' (Vd) = P(Vd)/Nd. Show that Vd is obtained graphically as the velocity %3D coordinate of the point where a line through the origin is tangent to the graph of P(v) as shown in the figure below. Power () Minimum power consumption Maximum distance traveled 10 15 Velecity (mis)
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