Can a cat ever catch a mouse in a circular maze?

[Davorak]

Just read Bartholomew's post oh well. Chronon did somthing like this:
<br /> \int \frac{1}{{\sqrt{c - a\,x^2}}} \,dx = \frac{\arcsin ({\sqrt{\frac{a}{c}}}\,x)}{{\sqrt{\Mfunction{a}}}}<br />
substitute in c\ for \ V^2 \ and \ a \ for \ \frac{r^2\,V^2}{R^2}
so using substituting in we get
<br /> \int \frac{1}{{\sqrt{V^2 - \frac{r^2\,V^2}{R^2}}}}\,dr = \frac{\arcsin (r\,{\sqrt{R^{-2}}})}{{\sqrt{\frac{{\Mfunction{V}}^2}{R^2}}}} = \frac{R\,\arcsin (r\,{\sqrt{R^{-2}}})}{V} = t<br />
Therefore
<br /> r = R\,\sin (\frac{t\,V}{R})<br />
<br /> r = R \ When \ \sin (\frac{t\,V}{R})=1<br />
Therefore
<br /> \frac{t\,V}{R} = \frac{\pi }{2}<br />
<br /> t = \frac{\pi \,R}{2\,V}<br />
I did not include \pm for square root or multiple solutions but in the end they do not matter.

I still like my idea of replacing with a force and using conservation of energy to show the cat will catch the mouse. If anyone would like to see it let me know.

 

[RandallB]

What if the mouse moves back and forth left to right without hitting the side of the circle? If the cat matches by moving sideways, the mouse can keep going forever. If the cat does not move side to side, what does it do? The claiming that it can now close in further does not necessarily make it so.

That's why it should keep on a line (radius) that runs from center to mouse.
Draw lines back from side to side limits of mouse to center. Cat will ALWAYS overrun the line unless he picks a point closer to the mouse no matter how small there will always be a point that is closer until he cacthes. Thus cat does follow a curve but one that bends up towards the mouse, as the mouse is on a curve the bends down towards the cat.