题目

Islamabad, Pakistan, June 22nd---Two mountain climbers surprisingly survived (幸免于) a fall of over 500 feet on the 25,530-foot mountain in Pakistan, Saturday. The two climbers were climbing an ice-covered wall of the mountain when they suddenly lost their footing and fell about 560 feet to a narrow snow-covered ledge(悬崖突出部分) below. “We were lucky that ledge was there,” said the climbers, “Otherwise, we would have fallen over 2,000 feet.” If the ledge had not been there, the two climbers almost certainly have met their death. “It’s a wonder,” the climbers said, 如图，在长方形ABCD中，AB＝2，BC＝1，E为DC的中点，F为线段EC(端点除外)上一动点．现将△AFD沿AF折起，使平面ABD⊥平面ABC．在平面ABD内过点D作DK⊥AB，垂足为K．设AK＝t，则t的取值范围是________．