Question

A tightrope is stretched 30 ft above the ground between the Jay and the Tee buildings, which are 50 feet apart. A tightrope walker, walking at a constant rate of 2 ft per sec from point A to point B, is illuminated by a spotlight 70 feet above point A. How fast is the shadow of the tightrope walker's feet moving up the wall of the Tee building when she is 10 feet from point B? (Indicate units of measure.)

Answer 1

So the question is, how fast is the the shadow moving up the wall as she walks, that is to say, what is the change in the position of the shadow as her position changes? If we call the P the position of the shadow (say, measured from 0 which we take to be the ground) and x the position of the person, then we seek to find dP/dx. If we can find an explicit relationship between P and x then we could simply take the derivative and evaluate at 40 (assuming x is measured from the Jay building). That is to say, for a fixed value of x, can you produce a formula which results in P?

Let's use the more suggestive picture below.