https://file.aiquickdraw.com/mathbot/file/17301694839782xlmq671.jpg

To find the center of gravity of this composite object, we can use the alternative method, which involves dividing the shape into simpler rectangular sections, calculating the area and centroid of each section, and then finding the weighted average positions.

### Steps:

1. **Divide the Shape:**
   - Let Section \( A \) represent the left rectangle.
   - Let Section \( B \) represent the tall rectangle on the right.

2. **Find the Area of Each Section:**
   - Area of Section \( A \): \( A_A = 16 \times 3 = 48 \) square units.
   - Area of Section \( B \): \( A_B = 4 \times 7 = 28 \) square units.

3. **Determine the Centroids of Each Section:**
   - For Section \( A \):
     - Horizontal centroid \( x_A = \frac{16}{2} = 8 \)
     - Vertical centroid \( y_A = \frac{3}{2} = 1.5 \)
   - For Section \( B \):
     - Horizontal centroid \( x_B = 16 + \frac{4}{2} = 18 \)
     - Vertical centroid \( y_B = \frac{7}{2} = 3.5 \)

4. **Calculate Weighted Average for Horizontal and Vertical Centers of Gravity:**

   Using the formulas for the composite center of gravity:

   \[
   x_{cg} = \frac{A_A \cdot x_A + A_B \cdot x_B}{A_A + A_B}
   \]
   \[
   y_{cg} = \frac{A_A \cdot y_A + A_B \cdot y_B}{A_A + A_B}
   \]

5. **Plugging in the Values:**
   - Horizontal Center of Gravity (\( x_{cg} \)):
     \[
     x_{cg} = \frac{(48 \times 8) + (28 \times 18)}{48 + 28} = \frac{384 + 504}{76} = \frac{888}{76} \approx 11.7
     \]
   - Vertical Center of Gravity (\( y_{cg} \)):
     \[
     y_{cg} = \frac{(48 \times 1.5) + (28 \times 3.5)}{48 + 28} = \frac{72 + 98}{76} = \frac{170}{76} \approx 2.2
     \]

### Final Answer:
- **Horizontal Center of Gravity:** \( \approx 11.7 \) (to the nearest tenth)
- **Vertical Center of Gravity:** \( \approx 2.2 \) (to the nearest tenth)

Would you like a deeper explanation of any part of this process?

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### Related Questions:
1. How do you calculate the center of gravity for an irregular shape?
2. How does the center of gravity change if Section B's height increases?
3. What is the difference between center of mass and center of gravity?
4. How would adding a third section affect the center of gravity calculation?
5. Can the center of gravity lie outside the actual material of the object?

### Tip:
For composite objects, always ensure to label each section, calculate its individual centroid, and use weighted averages to simplify the calculations for the center of gravity.

Find the Center of Gravity for the following object using the Alternative Method.

Learn how to calculate the center of gravity for a composite object by breaking it into simpler shapes. This problem involves determining the centroid and using weighted averages to find the horizontal and vertical centers of gravity.

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