Final answer:
The question involves using the concept of similar triangles to determine how the length of a man's shadow changes as he walks away from a light pole at a constant speed. The problem is a high school level mathematics question and applies proportions in the context of similar triangles.
Step-by-step explanation:
The subject of the question is Mathematics, and it pertains to the topic of similar triangles and proportions, which is typically covered in High School geometry classes. When the man walks away from the pole, the length of his shadow will increase as the distance between him and the street light increases. If we consider the man and the street light as the tops of two vertical poles, with their respective shadows on the ground forming right angles with the poles, we can see two right triangles forming that are similar by Angle-Angle (AA) similarity.
To find out how the length of the man's shadow changes over time, we can use the concept of similar triangles. The ratio of the height of the street light to the height of the man will be equal to the ratio of the length of the shadow cast by the light to the length of the shadow cast by the man. If we let x represent the length of the man's shadow at any given time, and y represent the distance of the man from the street light, we can set up a proportion:
\( \frac{11.0 ft}{5.7 ft} = \frac{y}{x} \)
Since the man is walking at a speed of 7.0 feet/sec, we know that y will increase by 7.0 feet every second. We can use this information, along with the proportion, to calculate the rate at which the man's shadow lengthens as he walks away from the pole.