Final answer:
The resultant force has a magnitude of 3.605 N.
Step-by-step explanation:
To find the resultant force, we need to add the two given forces together. The given force of 3.0 N acts at an angle of 30 degrees above the horizontal. We can break this force into horizontal and vertical components using trigonometry. The horizontal component is given by 3.0 N * cos(30 degrees) = 2.598 N, and the vertical component is given by 3.0 N * sin(30 degrees) = 1.5 N.
The gravitational force of 4.0 N acts downward, so its vertical component is -4.0 N. Adding the vertical components together gives 1.5 N - 4.0 N = -2.5 N. Adding the horizontal components together gives 2.598 N. The magnitude of the resultant force can be found using the Pythagorean theorem: √((2.598 N)² + (-2.5 N)²) = √(6.744 N² + 6.25 N²) = sqrt(12.994 N²) = 3.605 N.