1. **Problem Statement:** Determine the force in each member of the truss given loads $P_1 = 6$ kN and $P_2 = 9$ kN, and state whether each member is in tension or compression. 2. **Assumptions and Method:** We use the method of joints or sections to analyze the truss. Each joint must satisfy equilibrium: $$\sum F_x = 0, \quad \sum F_y = 0.$$ Members in tension pull away from the joint, members in compression push towards the joint. 3. **Step 1: Calculate support reactions.** Sum moments about one support to find vertical reactions. For example, if the truss is simply supported, use: $$\sum M_A = 0 \Rightarrow R_B = \frac{P_1 \times d_1 + P_2 \times d_2}{L}$$ where $d_1, d_2$ are distances from support A to loads, and $L$ is the total length. 4. **Step 2: Analyze each joint starting from supports.** At each joint, write equilibrium equations: $$\sum F_x = 0, \quad \sum F_y = 0$$ Solve for unknown member forces. 5. **Step 3: Determine tension or compression.** If the force direction assumed is away from the joint and the calculated force is positive, the member is in tension. If negative, it is in compression. 6. **Example:** Suppose member AB is horizontal and member AC is diagonal. At joint A: $$\sum F_x = 0: F_{AB} - \text{horizontal component of } F_{AC} = 0$$ $$\sum F_y = 0: R_A - P_1 - \text{vertical component of } F_{AC} = 0$$ Solve these for $F_{AB}$ and $F_{AC}$. 7. **Repeat for all joints** until all member forces are found. 8. **Final answer:** List each member with its force magnitude and state "tension" or "compression" based on sign. *Note:* Without the truss geometry and member layout, exact numeric answers cannot be provided here. Please provide a diagram or member lengths and angles for precise calculation.