Bird Flying Speed at 10m Altitude

[Jimmy Perdon]

A bird is flying at an altitude of 10m above you, his angular position from your point of view is changing at 0.5 rad · s^-1. How fast is the bird flying when he is directly above you?

 

[skeeter]

have you made a sketch? if so, do you see this relationship?

$\cot{\theta} = \dfrac{x}{10}$

where $\theta$ is the angle of elevation from the observer to the bird, and $x$ is the horizontal distance from the observer to the bird.

you are given $\dfrac{d\theta}{dt}$

differentiate implicitly with respect to time and determine $\dfrac{dx}{dt}$ when $\theta = \dfrac{\pi}{2}$

 

[Jimmy Perdon]

Thank you!