What is the resultant magnitude and direction of three coplanar forces of 40 N at 45 degrees east of south, 10 N west, and 70 N at 35 degrees east of north?

To determine the resultant magnitude and direction of the given forces, we need to break each force down into its components and then sum those components to find the overall resultant force.

1. The first force is 40 N at 45 degrees east of south. To find the components:

• The south component: ( 40 \cos(45^\circ) = 40 \times \frac{\sqrt{2}}{2} \approx 28.28 , \text{N south} )

• The east component: ( 40 \sin(45^\circ) = 40 \times \frac{\sqrt{2}}{2} \approx 28.28 , \text{N east} )

2. The second force is 10 N acting directly west. Thus:

• The west component: 10 N west.

3. The third force is 70 N at 35 degrees east of north. To find the components:

• The north component: ( 70 \cos(35^\circ) \approx 70 \times 0.819 = 57.33 , \text{N north} )

• The east component: ( 70 \sin