Question

A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 35 ft from the base of the pole?

Answer 1

The tip of the shadow is moving at `4.8 "ft"/"sec"`

Explanation:

Consider the situation as depicted in the image below:
Based on similar triangles we have
`color(white)("XXXX")(s(t))/6 = (s(t)+w(t))/16`

`rarrcolor(white)("XXXX")10s(t) = 6w(t)`

`rarrcolor(white)("XXXX")w(t) = 10/6s(t)`

We are told that a a certain time `t`
`color(white)("XXXX")(d(w(t)))/(dt) = 8 "feet"/"second"`

`(d(w(t)))/(dt) = (d(10/6s(t)))/(dt)`

`color(white)("XXXX")= 10/6(d(s(t)))/(dt)`

Therefore
`color(white)("XXXX")10/6 (d(s(t)))/(dt) = 8 "feet"/"second"`

`rarrcolor(white)("XXXX")(d(s(t)))/(dt) = 4.8 "feet"/"second"`