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|Outfoxing a fox (Posted on 2019-02-23)
A rabbit is trying to avoid detection by a nearby fox.
Initially, the fox and the rabbit are out of each other's sights as they are on opposite sides of a tree at the origin with the rabbit 1 unit North and the fox 1 unit South.
The fox starts to run directly to the left in a straight line with a constant speed 1 unit.
To avoid detection, the rabbit starts to run along a certain path with a constant speed 2 units, so as to always keep the tree between itself and the fox.
Find the differential equation which describes the path (in polar coordinates) of the hiding rabbit.
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