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The problem you're dealing with seems to involve finding the angle \( \theta \) required to make the resultant force act along the positive \( u \)-axis, with a given magnitude of 3.8 kN. You already have the magnitude of \( F_B \) as 1.92 kN from Part A. In Part B, you're attempting to determine the angle \( \theta \).

### Approach:

1. **Force Components:**
   - \( F_A = 3 \, \text{kN} \) acts horizontally along the \( x \)-axis.
   - \( F_B = 1.92 \, \text{kN} \) acts at an angle \( \theta \) to the horizontal (from the figure).
   
2. **Resultant Force along the \( u \)-axis:**
   The resultant force is the vector sum of \( F_A \) and \( F_B \), and it's required to lie along the positive \( u \)-axis with a magnitude of 3.8 kN.

3. **Resolve the Forces:**
   - Decompose both forces into their components along the \( x \)-axis and \( y \)-axis:
     - \( F_A \) is purely horizontal: \( F_A = (3 \, \text{kN}, 0) \).
     - \( F_B \) will have both \( x \)- and \( y \)-components depending on \( \theta \): 
       \[
       F_{Bx} = F_B \cos(\theta) = 1.92 \cos(\theta)
       \]
       \[
       F_{By} = F_B \sin(\theta) = 1.92 \sin(\theta)
       \]
       
4. **Resultant Force:**
   Since the resultant force is along the \( u \)-axis, its components along the \( x \)- and \( y \)-axes should satisfy the following:
   - The total force in the \( x \)-direction equals the component along \( u \)-axis: 
     \[
     F_{A} + F_{Bx} = 3.8 \cos(30^\circ)
     \]
   - The total force in the \( y \)-direction should equal the component along \( u \)-axis:
     \[
     F_{By} = 3.8 \sin(30^\circ)
     \]

5. **Solve for \( \theta \):**
   Using these two conditions, solve for \( \theta \). If you attempt the equation for the resultant components and solve algebraically, you'll arrive at the required angle.

Would you like me to provide the full solution for \( \theta \) based on this approach?

Determine the required magnitude of FB and the angle θ, given that the resultant force is required to act along the positive u-axis and have a magnitude of 3.8 kN.

Learn how to determine the required angle θ and the magnitude of FB in vector mechanics, where forces act at angles. This problem involves trigonometric identities, vector resolution, and the calculation of resultant forces along specified axes.

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