Final answer:
The distance between the dock and the boat is decreasing at the rate of 2 feet per second when the boat is 2 feet away from the dock, which is the same as the rate at which the rope is being pulled in.
Step-by-step explanation:
The question involves a scenario where a boat is being pulled toward a dock with a rope being pulled in at a rate of 2 feet per second. The distance between the dock and the boat is decreasing at the rate of 2 feet per second when the boat is 2 feet away from the dock, which is the same as the rate at which the rope is being pulled in.
To find how fast the distance between the dock and the boat is decreasing when the distance to the dock is 2 feet, we can apply the concept of related rates in calculus. Since the rope is being pulled in at a constant rate, the speed at which the boat approaches the dock is the same as the rate at which the rope is shortening when the boat is 2 feet from the dock.
Therefore, the boat is approaching the dock at 2 feet per second when it is 2 feet away from the dock.