Word Problem; Street light is at the top of a 15.500ft Pole

[killasnake]

I am always having trouble with word problems. I know I would have to draw the picture first but mostly after that I do not know what to do next.

A street light is at the top of a 15.500ft. tall pole. A man 6.400ft tall walks away from the pole with a speed of 3.500feet/sec along a straight path. How fast is the tip of his shadow moving when he is 42.00 feet from the pole?

 

[stapel]

Label things. For instance, label the height of the light with its (fixed) height, and the height of the man with his (fixed) height. Label the distance between the pole and the man as, say, "x", with dx/dt = 3.5. Label the length of the shadow as, say, "s".

You then have two triangles, necessarily similar. From these, you can create proportions:

. . . . .15/(x + s) = 6.4/s

Plug "42" in for "x", and solve for "s". This is the length of the shadow at the point in question.

Return to the above equation. You know dx/dt. Differentiate the above implicitly, and solve for ds/dt at x = 42.

Eliz.