Question

A street light is mounted at the top of a 12 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

16 ft/s.

Explanation:

`(dx)/(dt)=\text{Velocity of person}=8\ \text{ft/s}`

As the two triangles in the figure are similar to each other we have

`(12)/(y)=(6)/(y-x)\\\Rightarrow (2)/(y)=(1)/(y-x)\\\Rightarrow 2y-2x=y\\\Rightarrow y-2x=0\\\Rightarrow y=2x`

Differentiating with respect to time we have

`(dy)/(dt)=2(dx)/(dt)\\\Rightarrow (dy)/(dt)=2*8\\\Rightarrow (dy)/(dt)=16\ \text{ft/s}`

Rate at which the tip of the shadow moves away from the pole is 16 ft/s.