Final answer:
The magnitude of the resultant acceleration is approximately 2.872 m/s².
Step-by-step explanation:
To find the magnitude of the resultant acceleration, we need to calculate the net force acting on the sailboat. The net force is the vector sum of the forces acting on the sailboat. The force due to the ocean tide acts in the eastward direction, while the wind force acts toward the northwest (which can be broken down into its horizontal and vertical components).
To determine the net force, we need to resolve the wind force into its horizontal and vertical components. The horizontal component will oppose the force due to the ocean tide, while the vertical component will not contribute to the net force in the horizontal direction.
Given that the mass of the sailboat is 3000 kg, the eastward force due to the ocean tide is 4500 N, and the wind force has a magnitude of 5800 N directed toward the northwest, we can calculate the horizontal component of the wind force using trigonometry:
Horizontal component of wind force = 5800 N * cos(45°) ≈ 4116 N
Now, we can calculate the net force:
Net force = Force due to ocean tide + Horizontal component of wind force
Net force = 4500 N + 4116 N = 8616 N
Finally, we can use Newton's second law of motion, F = ma, to calculate the magnitude of the resultant acceleration (a):
8616 N = 3000 kg * a
a = 2.872 m/s²
Therefore, the magnitude of the resultant acceleration is approximately 2.872 m/s².