A street light is at the top of a 11 ft tall pole. A woman 6 ft tall walks away

Question

A street light is at the top of a 11 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 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?

Note: You should draw a picture of a right triangle with the vertical side representing the pole, and the other end of the hypotenuse representing the tip of the woman's shadow. Where does the woman fit into this picture? Label her position as a variable, and label the tip of her shadow as another variable. You might like to use similar triangles to find a relationship between these two variables.

Explanation / Answer

In your case x=35 ft, H=11ft, h=6 ft (wow!), v1=dx/dt=4 ft/s is the speed of the walker,
v=dX/dt is the speed of the tip of the shadow and it doesn't depend on the distance between the walker and the base of the pole. But the length of the shadow depends on that distance.

v=v1*H/(H-h)

= 4*11 / (11-6)

=8.8 ft/s

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