Chapter 4.5, Problem 62E

(a)

To determine

To find: The glide angle which is more efficient for a 200-gram animal to glide rather that walk.

(b)

To determine

To find: The threshold function $\theta =g\left(m\right)$ that gives the curve along which walking and gliding are equally efficient and also find that it is an increasing or decreasing function of body mass.

(c)

To determine

To explain: To make gliding more efficient than walking, do larger gliders have larger or smaller selection of glide angles than smaller gliders.

(d)

To determine

To sketch: The graph of $S\left(m,\theta \right)=8.46m^{\frac{2}{3}}-1.36m\tan \theta$ when $\theta ={25}^{\circ }$ and $0\le m\le 3000$ then find the values of the body mass $m$ for which the gliding more efficient.

(e)

To determine

To find: The value of body mass $m$ (call it $m^{*}$) at the glide angle $\theta ={25}^{\circ }$ maximize $S\left(m,{25}^{\circ }\right)$.

(f)

To determine

To explain: The value of mass $m^{*}$ defines in part (e), increases or decreases with increasing $\theta$  that is , as glider reduces its glide angle, does its optimal size become larger or smaller.

(g)

To determine

To find: The glide angle $\theta$ for which the gliding is more efficient than walking if Dumbo is a gliding elephant whose weight is 1 metric ton $\left({10}^6\mathrm{g}\right)$.