Solving Train & Camera Motion Questions: a & b

[yangxu]

Homework Statement

A train is traveling from left to right along a long straight horizontal track at 0.9km/min. A movie camera 1km away from the train is focused on the train.

a) How fast is the distance between the camera and the train changing when the train is 2km from the camera?

b) How fast is the camera rotating (in radians/min) at the moment when the train is 2km from the camera?

The Attempt at a Solution

I'm not sure how the equations should be written, most of the questions I've seen are lights on a pole (telling you its height and position) with an object moving toward or away from it, thus allowing trigonometric equations to be set up.

Part a) makes it sound like it's going to be a linear equation with no trigonometry involved, but part b) confuses me with the camera's rate of rotation. Any help on how I should write the equations for these two parts is highly appreciated. Thanks in advance.

 

[dynamicsolo]

I think the problem means for you to draw a line from the camera to a specific point on the train, say, the "nose" of the locomotive. However, something seems very sloppy about the way the problem is written. It seems they should mean that the perpendicular distance from the camera to the track is 1 km. Otherwise, you have no way to figure out distances and angles; also, the train is plainly not both 1 and 2 km. from the camera in the parts of the problem.

It will be important from here to draw a picture of the situation. There will now be a right triangle formed between camera, train, and closest point on the track.