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 farmerpig, 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 20081117 14:43:48 