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AP® Calculus AB-BC

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Angular Rate of Change

APCALC-XSZLXK

A squirrel is climbing up a tree attempting to escape from a dog that is sitting $5$ feet from the base of the tree. The position of the squirrel at any time $t>0$ is represented by the equation $h(t)=\frac{t}{2}+3.$

At the moment the squirrel is $5$ feet from the ground, how fast is the angle of elevation from the dog to the squirrel changing?

A

$\cfrac{1}{2}\ \text{radian/second}$

B

$\cfrac{1}{5}\ \text{radian/second}$

C

$\cfrac{\sqrt{2}}{10}\ \text{radian/second}$

D

$\cfrac{1}{20}\ \text{radian/second}$