Final answer:
The acceleration of the boat is approximately 0.778 m/s² north, calculated using Newton's second law with a net force of 210 N (after subtracting the opposing force from the water) and the boat's mass of 270 kg.
Step-by-step explanation:
The question is asking for the acceleration of a sailboat given a net force exerted on it by the wind and the water. To solve this, we can use Newton's second law of motion, F = ma, where F is the net force on the boat, m is the mass of the boat, and a is the acceleration. Here, we have a force of 390 N north exerted by the wind and opposing it is a force of 180 N south exerted by the water. The net force is therefore 390 N - 180 N = 210 N towards the north. With the mass of the boat being 270 kg, the acceleration a can be calculated by rearranging the formula to a = F/m.
Thus, the acceleration a = 210 N / 270 kg, which equals approximately 0.778 m/s² north. This demonstrates how the resultant force exerted by both the wind and the resistance from the water determines the acceleration of the sailboat in accordance with Newton's second law.