Flight and the Fourth Amendment

Sometimes, people run when they see you coming. May you chase them? If you do, does that amount to a "show of authority" constituting a detention, requiring reasonable suspicion? If they throw down contraband or a weapon during the chase and you recover it, is that the "fruit" of an illegal detention? Can they be arrested for illegal possession, or for resisting a lawful command to stop?As usual, the answer is, "It all depends." It depends on the circumstances at the start of the flight, actions