## Cat and mouse

Now here's a problem I thought up that I actually know the answer to

A cat and a mouse start at opposing points by the inside wall of a cylindrical box 1 meter in radius with sides too high to climb. The cat and mouse each move at a constant speed, and the cat always moves straight towards the mouse wherever the mouse is. When the cat gets within half a meter of the mouse, the cat leaps and catches the mouse. How much faster than the cat does the mouse have to be to perpetually evade capture?
 I don't understand the question. How exactly are the cat and mouse placed, and the tube?
 In the view from above, the box (open to the sky) appears as a circle--the cylindrical box is positioned like a grain silo. Pick a diameter of this circle. The cat starts at one end of the diameter, just within the box, and the mouse starts at the other end, also just within the box. The circle's edge is a vertical wall which the mouse can't climb.

Recognitions:
Gold Member
Staff Emeritus

## Cat and mouse

In other words, the cat and mouse are constrained within a unit circle.
 Basically, yes. I can't just _say_ they're stuck in a circle; cats and mice get stuck in boxes. Round boxes.

 Quote by Bartholomew How much faster than the cat does the mouse have to be to perpetually evade capture?
It's easy :

Vmouse > 2 * Vcat

 Well, if the cat's smart, the mouse has to be that fast. But in the problem the cat's dumb--he always goes straight towards the mouse.
 You are right! Then, probably Vmouse > Vcat * 2/sqrt(3) is enough.
 You got it Rogerio.