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:
Then I differentiated implicitly with respect to t:
And found x by plugging 3 into the original equation for z:
Then plugged x back into , and plugged in .5 for
However, this gave me the wrong answer, so I have no idea what to do.
I need help with BOTH part a and b. I'd really appreciate it!