Final answer:
The magnitude and direction of the combined force when two men push on a barrel at different angles can be determined by decomposing the forces into their eastward and northward components, summing these components, and then using the Pythagorean theorem and arctan to find the resultant force.
Step-by-step explanation:
To find the magnitude and direction of the combined force when two men are pushing on a barrel with forces at different angles, we use vector addition by components. For each force, we need to break it down into its eastward (x-axis) and northward (y-axis) components.
The first man's force has an eastward component of 6.00 N × cos(15°) and a northward component of 6.00 N × sin(15°). The second man's force has an eastward component of 4.50 N × cos(40°) and a southward component, which is the negative northward direction, of -4.50 N × sin(40°).
After calculating these components, we add the corresponding eastward components and northward components together to get the total force vector in component form. The magnitude of the resultant force is then found by applying the Pythagorean theorem to these total x and y components, and the angle of the resultant force can be found through the inverse tangent function, arctan(total y component/total x component).