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The force exerted by the wind on the sails of a sailboat is 390 N north. The water exerts a force of 180 N south against the boat. If the boat (including its crew) has a mass of 270 kg, What is the acceleration of the boat?

User Jmart
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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.

User GunJack
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