A 2m tall woman is running at a rate of 2 m/s when she spots a bird in a tree 6m off the ground. How fast is the angle of elevation to the bird increasing when she is 3m from the base of the tree?

Question

amistre64 · Answer

can you define an equation to model the situation?

amistre64 · Answer

|dw:1374688189518:dw|

amistre64 · Answer

$$tan(\alpha)=\frac4d$$

amistre64 · Answer

take the derivaitve
$$tan(\alpha)=\frac4d$$
$$sec^2(\alpha)~\alpha'=-\frac{4d'}{d^2}$$

amistre64 · Answer

we know d, we can readily calculate a, and we know d'

amistre64 · Answer

$$\alpha'=-\frac{4(-2)}{3^2}~(\frac{3}{5})^2$$
-2 since they are running towards the tree, or play with the sign

amistre64 · Answer

the closer you get, the faster yo have to look up a a fixed point i beleive