Chasing Person B: Describing the Curve Mathematically

[hypermonkey2]

Heres a problem that could use some light. Say person A at (0,1) is following a person B at (0,0). Person B moves horizontally with a constant speed v (towards the positive x direction). Person A also moves with speed v, but always in the direction pointing at person B (to chase him). How can we describe mathematically the curve thus created?

I hope my explanation of the problem was clear, thanks!

 

[Tide]

Do you think A will ever intercept B?

 

[hypermonkey2]

I wouldn't think so. Their distance might become infinitely small though, if that means the same thing.

 

[Tide]

So one property of the curve would be that it has an asymptote?

 

[hypermonkey2]

That would seem to be the case. But even so, we haven't been able to solve the differential equation. Can you try a mathematical analysis? This is not homework, haha, no need for the socratic method.

 

[TD]

Have a look at http://mathworld.wolfram.com/PursuitCurve.html" .

 

[hypermonkey2]

thanks, ill wrestle with that.