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Transcribed Image Text:**Question 7**
Three forces with magnitudes 70 pounds, 100 pounds, and 20 pounds act on an object at angles 50°, -40°, and 110° respectively, with the positive x-axis. Find the direction and magnitude of the resultant force. Draw a diagram of your analysis, and include the resultant force.
**Analysis:**
To solve this problem, we need to determine the components of each force in the x and y directions, sum these components, and then find the magnitude and direction of the resultant force.
### Step-by-Step Solution:
1. **Resolve each force into x and y components using trigonometry:**
- **Force \( F_1 \) (70 pounds at 50°):**
\( F_{1x} = 70 \cos(50°) \)
\( F_{1y} = 70 \sin(50°) \)
- **Force \( F_2 \) (100 pounds at -40°):**
\( F_{2x} = 100 \cos(-40°) \)
\( F_{2y} = 100 \sin(-40°) \)
- **Force \( F_3 \) (20 pounds at 110°):**
\( F_{3x} = 20 \cos(110°) \)
\( F_{3y} = 20 \sin(110°) \)
2. **Calculate the numerical values of the components:**
Use a calculator (ensure it is in degree mode):
- \( F_{1x} = 70 \cos(50°) \approx 45 \)
- \( F_{1y} = 70 \sin(50°) \approx 54 \)
- \( F_{2x} = 100 \cos(-40°) \approx 77 \)
- \( F_{2y} = 100 \sin(-40°) \approx -64 \)
- \( F_{3x} = 20 \cos(110°) \approx -7 \)
- \( F_{3y} = 20 \sin(110°) \approx 19 \)
3. **Sum the x and y components:**
- \( R_x = F_{1x} + F_{2x} + F_{3x} \)
\( R
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