Question

导数英文数学题，求过程~

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.

Answer 1

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