A street light is at the top of a 11 foot tall pole.A 6 foot tall woman walks away from the pole wit

题目

A street light is at the top of a 11 foot tall pole.A 6 foot tall woman walks away from the pole with a speed of 5 ft/sec along a straight path.How fast is the tip of her shadow moving when she is 30 feet from the base of the pole?
The tip of the shadow is moving at ft/sec.

答案

设妇女与电线杆之间的距离为x,妇女的影子长为y；
则根据题意：11/(x+y)=6/y
解得：y=(6/5)x
妇女头部的影子与电线杆之间的距离为 x+y=(11/5)x
两边对t求导,得：(x+y)'=(11/5)x'
现x'=5
所以：(x+y)'=(11/5)•5=11
The tip of the shadow is moving at 11 ft/sec