Answer:
The force exerted by the ocean tide is directed to the right (east).
The force exerted by the wind is directed to the northwest (45° N of W).
We should separate the x- and y- components of the wind force, and evaluate each component separately.
[tex]F_x = 6000\cos(\pi/4)(-\^{x})\\F_y = 6000\sin(\pi/4)(+\^{y})[/tex]
We denote the direction to the right as the positive direction, so the x-component of the wind force is in the negative direction.
The resultant force is as follows:
[tex]F_R = [2000 - 4242.64](\^{x}) + [4242.64](\^{y})\\F_R = -2242.64\^{x} + 4242.64\^{y}[/tex]
The resultant acceleration can be found by Newton's Second Law:
[tex]F = ma\\\\a_R = F_R/m = -1.12\^{x} + 2.12\^{y}[/tex]
The magnitude of the resultant acceleration is
[tex]|a_R| = \sqrt{(1.12)^2 + (2.12)^2} = 2.4 ~m/s^2[/tex]
