An object acted on by three forces moves with constant velocity. One force acting on the object is in the positive x direction and has a positive magnitude of 6.7N; a second force has a magnitude of 4.6 N and points in the negative y direction. (1)"Find magnitude of the third force acting on the object.

(2) Find the direction of the third force acting on the object in terms of pheta=-----------degrees from the + x direction.

see above . Check my work.

1.7

To find the magnitude of the third force acting on the object, we need to use the fact that the object is moving with constant velocity. This means that the net force acting on the object must be zero.

To find the net force, we can add the individual forces acting on the object. The force in the positive x direction has a magnitude of 6.7 N, and since it's in the positive x direction, it will have a positive sign. The force in the negative y direction has a magnitude of 4.6 N, and since it's in the negative y direction, it will have a negative sign. Let's call the magnitude of the third force "F":

Net force = Force in x direction + Force in y direction + F

Since the object is moving with constant velocity, the net force is zero:

0 = 6.7 N - 4.6 N + F

Simplifying the equation:

F = 4.6 N - 6.7 N

F = -2.1 N

Therefore, the magnitude of the third force acting on the object is 2.1 N.

Now, to find the direction of the third force in terms of theta (θ) measured from the +x direction, we can use trigonometry. Since we have the force components in x and y directions, we can use the inverse tangent (arctan) function to find the angle:

θ = arctan (Force in y direction / Force in x direction)

θ = arctan (-4.6 N / 6.7 N)

Using a calculator, we can find:

θ ≈ -36.4 degrees

Therefore, the direction of the third force acting on the object, measured from the +x direction, is approximately -36.4 degrees.