A fox moving at a constant speed of s m/s wants to eat a duck that is swimming at 1 m/s in a pond. The duck can only fly when he’s on land, and the fox can’t swim.
What is the maximal value of s such that wherever the animals start, the duck can reach land without being caught by the fox?
Assumptions:
- The pond is a perfectly round circle.
- The fox can start anywhere except inside the pond, but he can never enter the pond.
- The duck must start somewhere on the pond.
- If the duck reaches the edge of the pond at the exact same time as the fox, the fox catches the duck.
- If the duck reaches land and the fox is not there, he instantly flies away and the fox loses his meal.
- The duck and the fox see each other and take decisions in real time.