Question - Determining the Resultant Force and its Direction

To find the magnitude of the resultant force, we can break the forces into their x and y components. For the 600 N force:

\[ F_{x1} = 600 \cos(30^\circ) \]

\[ F_{y1} = 600 \sin(30^\circ) \]

For the 800 N force, which is purely in the y-direction:

\[ F_{x2} = 0 \]

\[ F_{y2} = 800 \]

Now, add the x-components and y-components of the forces to find the resultant:

\[ R_x = F_{x1} + F_{x2} \]

\[ R_y = F_{y1} + F_{y2} \]

Substitute the values to find \( R_x \) and \( R_y \):

\[ R_x = 600 \cos(30^\circ) \]

\[ R_y = 600 \sin(30^\circ) + 800 \]

Use the Pythagorean theorem to find the magnitude of the resultant force (R):

\[ R = \sqrt{R_x^2 + R_y^2} \]

Calculate the angle (\( \theta \)) from the positive x-axis:

\[ \theta = \arctan\left(\frac{R_y}{R_x}\right) \]

Solve for \( R \) and \( \theta \) to get the magnitude and direction of the resultant force.