Final answer:
A) 950 N, 135° N of E, to find the resultant force using the polygon method, resolve the forces into their x and y components. Then, add up the x and y components to find the net force. Finally, use the magnitude and direction of the net force to determine the resultant force.
Step-by-step explanation:
To find the resultant force using the polygon method, we need to determine the x and y components of each force. Let's start by resolving the forces:
- Force A = 300 N, 30° N of E has an x-component of 300 * cos(30°) = 300 * √3/2 = 300√3/2 and a y-component of 300 * sin(30°) = 300 * 1/2 = 150
- Force B = 600 N, 270° has an x-component of 0 (since it acts in the west direction) and a y-component of -600 (since it acts downward)
- Force C = 100 N, due east has an x-component of 100 and a y-component of 0
Next, we add up the x and y components to find the net force:
- x-component of net force = 300√3/2 + 0 + 100 = 300√3/2 + 100
- y-component of net force = 150 - 600 + 0 = -450
Lastly, we use the magnitude and direction of the net force to find the resultant force:
- Magnitude of net force = √[(300√3/2 + 100)² + (-450)²]
- Direction of net force = arctan(-450 / (300√3/2 + 100))
Calculating the values gives us a resultant force of approximately 950 N and a direction of approximately 135° N of E.