Chapter 4.6, Problem 67E

To determine

(a)

To show that at a velocity v, the pigeon can fly a total distance $D(v)=(5\times {10}^4)v/P(v)$.

To determine

(b)

To find the volume $v_p$ that minimizes $P$.

To determine

(c)

To show that the velocity $v_d$ which maximizes $D\left(v\right)\text{satisfies}P\text{'}(v_d)=\frac{P(v_d)}{v_d}$.

To determine

(d)

To find the volume that maximizes distance traveled rather than minimizes power consumption.