1. ## Related Rates Problem

Hi, I've got a related rates problem I can't solve:
There is a dog and a cat. Initially the cat is located at (0,0) and the dog at (0, -a). The cat is moving along the x axis in the positive direction with a constant speed c. The dog is moving with a constant speed h, but its direction is always directly towards the cat. Identify the function y = f(x) that describes the trajectory of the dog.

2. Originally Posted by MrDiSante
Hi, I've got a related rates problem I can't solve:
There is a dog and a cat. Initially the cat is located at (0,0) and the dog at (0, -a). The cat is moving along the x axis in the positive direction with a constant speed c. The dog is moving with a constant speed h, but its direction is always directly towards the cat. Identify the function y = f(x) that describes the trajectory of the dog.
Let the following be displacement functions:

$cat(x)=cx$
$dog(x)=g(x)x-a$

Where the dog's velocity is:

$g(x) = h, dog(x) \le cat(x)$
$g(x) = -h, dog(x) > cat(x)$

The inequalities can go either way since there is no information on the dog's velocity when the dog and the cat are in the same position. The speed must be h, but the velocity can be plus or minus.