Chapter 2 - Derivatives - Review - Exercises - Page 199: 81

$400$ $ft/h$

We are given $\frac{dθ}{dt}$ = $-0.25$ $rad/h$ $\tan\theta$ = $\frac{400}{x}$ $x$ = $400\cot\theta$ $\frac{dx}{dt}$ = $-400\csc^{2}\theta\frac{d\theta}{dt}$ when $\theta$ = $\frac{\pi}{6}$ $\frac{dx}{dt}$ = $-400(2)^{2}(-0.25)$ = $400$ $ft/h$