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Bird Migration Power P is the rate at which energy E is consumed per unit time. Ornithologists have found that the power consumed by a certain pigeon flying at velocity v m/sv \mathrm{~m} / \mathrm{s} is described well by the function P(v)=17v1+103v3 J/sP(v)=17 v^{-1}+10^{-3} v^3 \mathrm{~J} / \mathrm{s}. Assume that the pigeon can store 5×104 J5 \times 10^4 \mathrm{~J} of usable energy as body fat. (a) Find the velocity vpmin v_{\text {pmin }} that minimizes power consumption.


Answered 2 years ago

Note that the birds will exhaust their energy after

T=5104 joulesP(v) joules/sec=5104P(v) secT= \dfrac{5\cdot10^4 \text{ joules}}{P(v) \text{ joules/sec}}=\dfrac{5\cdot10^4}{P(v)} \text{ sec}

Then, the total distance traveled after using their stored energy is


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