Optimization problem: speed of tip of shadow when 40 ft from

[agilder23]

A street light is mounted at the top of a 15 foot tall pole. A man 6feet tall walks away from the pole with a speed of 5 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 feet from the pole?

I started out trying to draw the man and the triangle associated with the shadow and his height, but it's not seeming to work. I don't know how to draw on here because this is one of my first times posting on here. Can somebody reply as soon as possible. I have a test in a couple of hours. Please and thank you for any help!

 

[BigGlenntheHeavy]

Draw a right triangle and inside draw another right triangle. Label one of the parallel legs in the first triangle 15 ft (light), in the second 6 feet (man) parallel to the first. Then the total length of the base is s. The length between the two legs is x an s-x.

Hence by similiar triangles we have (s-x)/6 =s/15, s = (5/3)x.

Ergo ds/dt =(5/3)dx/dt. Given that dx/dt = 5, we have ds/dt = (25/3) ft./sec.

That is the rate the tip of his shadow is moving

Note; The measurement 40 ft given in this problem is a "red herring" since the distance from the base of the light does not affect ds/dt.

Also note: This is a related rate problem, not an optimization one.