A farmer wants to catch a pig which is 100 meters away from him. They start running at the same time. The pig runs straight ahead, initially perpendicular to the line farmer-pig, at constant speed. The farmer always runs in the direction where he sees the pig (also at constant speed).

If the ratio of the speeds is 3:1 (farmer:pig), how far would the pig have traveled till the farmer caught it?

the farmers path can be defined by the differential equation

x*y''-(1/3)*sqrt(1+y'^2)=0

with y(100)=0 and y'(100)=0 this gives

y(x)=(3*100^(1/3)/2)*x^(2/3)-(3/8)*100^(-1/3)*x^(4/3)-112.5

so when x=0 y=-112.5 so when the farmer finally catches the pig, the pig will have traveled 112.5 meters

Posted by Daniel on 2008-11-17 14:43:48