Final answer:
The question asks how fast the tip of a man's shadow is moving as he walks away from a streetlight, which can be solved by leveraging the concepts of similar triangles and calculating the related rates of change.
Step-by-step explanation:
The question involves using the concepts of similar triangles and the rates of change to solve a related rates problem in mathematics. The problem presents a scenario where a man's shadow is created by a streetlight as he walks away from it. The man's height, the height of the streetlight, the man's walking speed, and the distance from the streetlight are given. We want to determine the speed at which the tip of the shadow is moving.
To find the speed at which the tip of the man's shadow is moving, we can use the properties of similar triangles to relate the man's height to the length of the shadow and the height of the streetlight. If we denote the distance between the man and the pole as x, the length of the shadow as y, the man's height as 6 ft, and the streetlight height as 17 ft, we have the proportional relationship 6/17 = y/(x+y).
By differentiating both sides concerning time t, and given that dx/dt is 4.0 feet/sec, we can solve for dy/dt, which gives us the rate at which the shadow's length is changing. Inserting all known values, we can calculate the velocity of the shadow's tip.