Try googling pursuit curve for some leads on this (and some nice animated graphics).
Can anyone help me with this:
We have a room H deep and W wide. In the far right corner is a mousehole. The cat starts in the bottom left corner, and the mouse starts in the top left corner i.e. cat starts at (0,0) and mouse at (0,H), and the mouse hole is at (W,H).
The cat starts to chase the mouse and always runs directly at the mouse. The mouse runs straight for the hole i.e. along the top wall from (0,H) towards (W,H).
The cat has a constant speed, so too does the mouse. These speeds are different.
Questions: what must the speed of the cat be (in terms of the speed of the mouse and the dimensions of the room) for it to catch the mouse before it reaches the hole. What is the equation that describes the cats path ? How far does the cat run if it does catch the mouse ?
All help greatly appreciated...