The wind exerts a force of 280 N North on a sailboat, while the water exerts a force of 131 N West on the sailboat. How many degrees west of north is this net external force directed?

To find the direction of the net external force, we can use trigonometry.

Let's consider the forces acting on the sailboat. The force exerted by the wind is acting to the North, and the force exerted by the water is acting to the West. We want to find the direction of the resultant force.

Using vector addition, we can combine the wind and water forces to find the resultant force acting on the sailboat.

The resultant force in the North direction is equal to the force exerted by the wind (280 N).

The resultant force in the West direction is equal to the force exerted by the water (131 N).

Now, we can find the magnitude and direction of the resultant force using the Pythagorean theorem and trigonometry.

Magnitude of the resultant force (F_res) = √(280^2 + 131^2) = √(78400 + 17161) = √95561 ≈ 309.21 N

To find the direction of the resultant force, we can use the tangent function:

tan(θ) = (force in the West direction) / (force in the North direction)
tan(θ) = 131 N / 280 N

Taking the inverse tangent of both sides to solve for θ, we have:

θ = arctan(131/280) ≈ 25.55 degrees

Therefore, the net external force is directed approximately 25.55 degrees West of North.

To determine the direction of the net external force, we can use trigonometry. Let's break down the forces given:

- The wind exerts a force of 280 N north.
- The water exerts a force of 131 N west.

Now, we can visualize the forces on a coordinate plane. Assume that north is the positive y-direction and west is the negative x-direction.

The wind force, exerted north, can be represented as (0, 280) on the coordinate plane. Similarly, the water force, exerted west, can be represented as (-131, 0) on the coordinate plane.

To find the net external force, we need to calculate the vector sum of these two forces. Adding them together, we get a resultant force of (-131, 280).

Now, we need to find the angle this resultant force makes with the north direction. We can use the tangent function to calculate this angle. The formula for the tangent of an angle, given the ratio of sides, is:

tan(angle) = (opposite / adjacent)

In our case, the opposite side is 280 N (north) and the adjacent side is -131 N (west).

Therefore, the tangent of the angle we are looking for is:

tan(angle) = (280 / -131)

Now we can solve for the angle by taking the inverse tangent (arctan) of both sides:

angle = arctan(280 / -131)

Using a calculator, we find that arctan(280 / -131) is approximately -64.5 degrees.

Since we are looking for the angle west of north, we take the absolute value of the result:

angle = |-64.5| ≈ 64.5 degrees.

Thus, the net external force is directed approximately 64.5 degrees west of north.