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.

问题描述：

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

先简单翻译一下这道题，电线杆 11foot 高，一个女人6 foot高，女人行走的速度是5foot/s
离电线杆30foot 的时候，他的头部的影子的速度是多少？
这道题用倒数定义做比较简单
设电线柱的坐标为原点，头部的影子的坐标为x
则使用相似三角形 (x-30)/x =6/11 解得 x=66
当过了dt时间女人移动了5*dt foot ，设影子的坐标为 s
(s-30-5*dt)/s=6/11 解得 s=66+11dt
在dt 时间内影子移动的距离为 s-66=11dt
速度=距离/时间所以 v=11dt/dt =11
答案为 The tip of the shadow is moving at 11 ft/sec.
竟然是英文题呵呵

答

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

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.

相关推荐