To find the resultant acceleration, we first need to calculate the net force acting on the sailboat.
The eastward force of 2000 N and the northwest wind force can be broken down into their components:
- The eastward force of 2000 N has no vertical component and only acts in the positive x-direction.
- The northwest wind force of 6000 N can be broken down into its northward and westward components using trigonometry:
F_west = 6000 N * cos(45°) = 4242.64 N
F_north = 6000 N * sin(45°) = 4242.64 N
The net force in the x-direction is:
Net Fx = 2000 N + F_west = 2000 N + 4242.64 N = 6242.64 N
The net force in the y-direction is:
Net Fy = F_north = 4242.64 N
The net force can then be calculated using Pythagorean theorem:
|Net F| = sqrt(Net Fx^2 + Net Fy^2)
|Net F| = sqrt((6242.64 N)^2 + (4242.64 N)^2)
|Net F| = sqrt(38970183.20 N^2 + 18012357.26 N^2)
|Net F| = sqrt(56982540.46 N^2)
|Net F| = 7544.81 N
Finally, we can calculate the acceleration using Newton's second law:
F = m*a
a = F/m
a = 7544.81 N / 2000 kg
a ≈ 3.77 m/s^2
Therefore, the magnitude of the resultant acceleration of the sailboat is approximately 3.77 m/s^2.
A 2000-kg sailboat experiences an eastward force of 2000 N by the ocean tide and a wind force against its sails with magnitude of 6000 N directed toward the northwest (45° N of W). What is the magnitude of the resultant acceleration?
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