Problem 54670. Solve an ODE: precocious pair’s porcine pursuit
In our previous encounters with Matilda and Labrun, the scintillating siblings collected candy wrappers, amused others with card tricks, and found interesting relations involving house numbers on their street.
But now their pet pig has run away, and the pair must catch her! They start a distance d away from the pig, which runs at speed V in a direction perpendicular to the line connecting the initial positions of the pig and the siblings. Matilda and Labrun run at speed v, always in a direction pointing at the current position of the pig.
Write a function that takes the distance d and the two speeds and returns the time required for Matilda and Labrun to catch their pet. Return Inf if the pair will not catch the pig, and please ignore the impracticality of reporting times to the nearest microsecond.
This problem is adapted from a problem in Advanced Mathematical Methods for Scientists and Engineers by Bender and Orzsag.
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