Final answer:
The sailboat accelerates at approximately 1.048 m/s² in a direction of 25.85° east of north, resulting from the combined force of the wind and water acting on the boat with a mass of 350 kg.
Step-by-step explanation:
To find the magnitude and direction of the acceleration of the sailboat, the applied forces and the mass of the sailboat must be taken into account. There is a 330 N force northward from the wind and a 160 N force eastward from the water. These forces can be treated as vectors and combined using Pythagorean theorem to find the resultant force acting on the boat.
The magnitude of the resultant force (Fnet) can be calculated as follows:
Fnet = sqrt((330 N)2 + (160 N)2) = sqrt(108900 + 25600) N = sqrt(134500) N ≈ 366.88 N
Next, to find the acceleration (a) we use Newton's second law:
a = Fnet / m
Where:
- Fnet is the net force
- m is the mass of the sailboat
Substituting the given values:
a = 366.88 N / 350 kg ≈ 1.048 m/s2
The direction of acceleration can be found using the arctangent of the force components:
θ = arctan(160 N / 330 N) ≈ 25.85°
This angle is measured from the north towards the east. Therefore, the boat accelerates at approximately 1.048 m/s2 in a direction of 25.85° east of north.