Thread: Application of Calculus problem

A street light is at the top of a 14 ft tall pole. A woman 6 ft tall 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 ft from the base of the pole?


This is a problem where they give you what I believe is a dv/dt of 5 ft/s, but I don't know what I have to do to find the speed of the tip of her shadow. I tried drawing triangles, but I don't know exactly what I need to do, and I can't think of any equation that would help me find this, y = mx+b since it's a straight line???

Hello, kycon90!

Did you make a sketch?

A streetlight is at the top of a 14 ft tall pole.
A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec.
How fast is the tip of her shadow moving when she is 30 ft from the base of the pole?

Code:

    A o
      |   * - C
      |       o
      |       |   *
    14|       |       *
      |      6|           *
      |       |               *
      |       |                   *
    B o-------o-----------------------o E
      : - x - D - - -  s-x  - - - - - :
      : - - - - - - s - - - - - - - - :

The lightpole is:

The woman is:
Her distance from the pole is:

The tip of her shadow is ft from the pole: .
. . Hence: .

Since , we have: .

Differentiate with respect to time: .


Therefore: .