A man stands at the junction of two perpendicular roads,

Chapter 1, Problem 1.100

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A man stands at the junction of two perpendicular roads, and his dog is watching him from one of the roads at a distance A feet away. At some time, the man starts to walk with constant speed v along the other road, and at the same time, the dog begins to run toward the man with a speed of 2v. Determine the path the dog will take, assuming that it always moves so that it is facing the man. Also determine when the dog will eventually catch the man.

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