**Problem:**

A train is traveling

0.5 km/min along a straight track, moving in the direction as shown in the figure below. A movie camera, 0.5 km away from the track, is focused on the train.

(a) How fast is the distance from the camera to the train changing when the train is

3 km from the camera? Give your answer to 3 decimal places.

(b) How fast is the camera rotating at the moment when the train is

3 km from the camera? Give your answer to 3 decimal places.

**What I've done:**

Well I tried to solve for the first question by using the Pythagorean theorem:

[tex]

x^2 + .5^2 = z^2[/math

$\displaystyle z = \sqrt{x^2 + .25}$

Then I differentiated implicitly with respect to t:

$\displaystyle

\frac{dz}{dt} = \frac{x \frac{dx}{dt} }{\sqrt{x^2 + .25}}$