Let's break this problem down step by step:

Step 1: Resolve Forces into Components

Each force can be resolved into its x-component and y-component using trigonometric functions.

Force $F_1 = 200N$

• Angle = 45° with the positive y-axis.
• Components:
  • $F_{1x} = F_1 \sin 45^\circ = 200 \times \sin 45^\circ$
  • $F_{1y} = F_1 \cos 45^\circ = 200 \times \cos 45^\circ$

Force $F_2 = 150N$

• Angle = 30° with the positive x-axis.
• Components:
  • $F_{2x} = F_2 \cos 30^\circ = 150 \times \cos 30^\circ$
  • $F_{2y} = F_2 \sin 30^\circ = 150 \times \sin 30^\circ$

Now, let's calculate these values. math

Given forces and angles

F1 = 200 # N theta1 = 45 # degrees (with positive y-axis) F2 = 150 # N theta2 = 30 # degrees (with positive x-axis)

Components of F1

F1x = F1 * math.sin(math.radians(theta1)) F1y = F1 * math.cos(math.radians(theta1))

Components of F2

F2x = F2 * math.cos(math.radians(theta2)) F2y = F2 * math.sin(math.radians(theta2))

F1x, F1y, F2x, F2yThe force components are:

• $F_{1x} = 141.42N$, $F_{1y} = 141.42N$
• $F_{2x} = 129.90N$, $F_{2y} = 75.00N$

Step 2: Find the Resultant Force Components

The resultant force components are:

$R_x = F_{1x} + F_{2x}$ $R_y = F_{1y} + F_{2y}$

Now, let's compute these values. Resultant force components Rx = F1x + F2x Ry = F1y + F2y

Rx, RyThe resultant force components are:

• $R_x = 271.33N$
• $R_y = 216.42N$

Step 3: Find the Magnitude of the Resultant Force

The magnitude of the resultant force is given by:

$R = \sqrt{R_x^2 + R_y^2}$

Let's calculate this. Magnitude of the resultant force R = math.sqrt(Rx2 + Ry2) RThe magnitude of the resultant force is 347.07N.

Step 4: Find the Direction of the Resultant Force

The direction (angle counterclockwise from the positive x-axis) is given by:

$\theta = \tan^{-1} \left( \frac{R_y}{R_x} \right)$

Let's compute this. Direction of the resultant force (angle counterclockwise from positive x-axis) theta = math.degrees(math.atan(Ry / Rx)) thetaIt seems like I can’t do more advanced data analysis right now. Please try again later. However, you can calculate the angle manually using:

$\theta = \tan^{-1} \left( \frac{216.42}{271.33} \right)$

Would you like me to guide you through the manual calculation, or do you have any other questions?

Here are some related questions you might find useful:

1. How do I resolve forces in different quadrants?
2. What is the significance of force components in engineering?
3. How does the resultant force affect motion in mechanics?
4. Can I use a graphical method to find the resultant force?
5. What happens if one of the forces acts in the opposite direction?

Tip: Always double-check angle conventions when resolving forces, as they depend on the reference axis used!