Final answer:
The rate at which the bottom of the ladder is moving away from the wall is approximately 0.769 feet/sec.
Step-by-step explanation:
In order to find the rate at which the bottom of the ladder is moving away from the wall, we can use the concept of similar triangles.
The ladder forms a right triangle with the wall, so we can use the properties of similar triangles to find the relationship between the rate at which the ladder is sliding down the wall and the rate at which the bottom of the ladder is moving away from the wall.
Let's call the distance between the bottom of the ladder and the wall x.
The length of the ladder is 13 feet. Since the ladder is sliding down the wall at a rate of 2 feet/sec, the rate at which the top of the ladder is moving down the wall is also 2 feet/sec.
Using the concept of similar triangles, we can set up the following proportion:
2 feet/sec / 13 feet = x feet/sec / 5 feet
Solving for x, we find that the rate at which the bottom of the ladder is moving away from the wall is approximately 0.769 feet/sec.