**Title: Understanding the Relationship Between Winch Speed and Boat Speed****Introduction:**A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat.**Diagrams and Explanation:**A diagram is provided which shows a boat being pulled towards a dock by a winch. The winch is positioned 12 feet above the deck of the boat and pulls in the rope at a rate of 4 feet per second. In the diagram, the distance from the dock to the boat along the waterline is represented as \( y \).![Diagram Description]- The winch is highlighted, positioned 12 feet above the boat.- The rope and its pulling direction are indicated.- The distance \( y \) represents the distance between the dock and the boat on the waterline.**Problem (a):**The winch pulls in rope at a rate of 4 feet per second. Determine the speed of the boat when there is 15 feet of rope out.\[ \_\_\_\_\_ \text{ ft/sec} \]Incorrect Answer: \( \times \)*Question: What happens to the speed of the boat as it gets closer to the dock?*Dropdown Answer: - The correct answer selected is "increases". - Correct Indicator: \( \checkmark \)**Problem (b):**Suppose the boat is moving at a constant rate of 4 feet per second. Determine the speed at which the winch pulls in the rope when there is a total of 15 feet of rope out.\[ \_\_\_\_\_ \text{ ft/sec} \]Incorrect Answer: \( \times \)*Question: What happens to the speed at which the winch pulls in rope as the boat gets closer to the dock?*Dropdown Answer: - The correct answer selected is "approaches 0".- Correct Indicator: \( \checkmark \)**Explanation:**- As the boat approaches the dock, the speed of the boat increases due to the decreasing angle of the rope which causes a more substantial horizontal component of the winch’s pulling speed.- Conversely, the speed at which the winch pulls in rope approaches zero because the rope length does not need to be adjusted as quickly when the boat is near the dock.**Conclusion:**Understanding the relationship between the winch speed and the boat speed is essential for docking safely and efficiently. The diagram and

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A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat. 14 ft/sec 12 ft Not drawn to scale (a) The winch pulls in rope at a rate of 4 feet per second. Determine the speed of the boat when there is 15 feet of rope out. ft/sec X What happens to the speed of the boat as it gets closer to the dock? The speed of the boat increases as it approaches the dock. (b) Suppose the boat is moving at a constant rate of 4 feet per second. Determine the speed at which the winch pulls in rope when there is a total o 15 feet of rope out. ft/sec X What happens to the speed at which the winch pulls in rope as the boat gets closer to the dock? The speed at which the winch pulls in rope approaches 0