The problem comes from Elementary Calculus an Infinitesimal Approach p.125:
9) A ball is dropped from a height of 100 ft, at which time its shadow is 500 ft from the ball. How fast is the shadow moving when the ball hits the ground? The ball falls with velocity 32 ft/sec, and the shadow is cast by the sun.
The answer (stated in book) is: $160\sqrt{6}$
I tried to solve it using similar triangles and I got: $64\sqrt{6}$, assuming the triangle formed by the ball and its shadow is a similar triangle (to the one when the ball is just realeased) as it falls. This approach appears correct but it yields the wrong answer.
I really ran out of ideas on how to solve this thing, so help me please :)
The problem is that the question is wrong. If the ball is falling at 32 ft/s when it hits the ground then your answer is correct. However, you're supposed to work out how fast the ball is falling yourself. The acceleration due to gravity is approximately $32 ft/s^2$. If you use that as the acceleration due to gravity, and ignore air resistance, you get the textbook answer.