Puzzle #11 – Terra Fermat

I recently watched The Hunger Games: Catching Fire. By means of a convenient plot device, Katniss ends up back in the arena. She is immediately presented with a test of her physical intuition.

odds

In the centre of the arena is a circular lake. The lake is divided into twelve circular sectors of equal size by rocky pathways. The pathways converge on an island bearing the cornucopia, housing a bounty of weaponry.

The twenty-four tributes start in one of the circular sectors on a small pedestal, some distance from the cornucopia.

Suppose Katniss can swim at speed u and run at speed v. For simplicity we’ll assume both u and v are constant. Assume also that v>u.

 

Question: At what angle should Katniss approach the nearest rocky pathway such that she reaches the cornucopia in the least possible time?

Hint: It is easiest to define the angle as being that which Katniss’ path subtends with the normal to the pathway.

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One thought on “Puzzle #11 – Terra Fermat

  1. Pingback: Terra Fermat Solution | Conversation of Momentum

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