Given weights A (135 pounds at 15 inches aft of datum), B (205 pounds at 117 inches aft of datum), and C (85 pounds at 195 inches aft of datum), where would the CG be located?

To determine the center of gravity (CG) location, you need to calculate the weighted average of all the weights in relation to their distances from the datum. This involves using the formula:

[ \text{CG} = \frac{\sum ( \text{weight} \times \text{distance from datum})}{\sum \text{weight}} ]

First, calculate the moment (weight multiplied by distance) for each weight:

1. For weight A: ( 135 , \text{lbs} \times 15 , \text{inches} = 2025 , \text{in-lbs} )

2. For weight B: ( 205 , \text{lbs} \times 117 , \text{inches} = 23985 , \text{in-lbs} )

3. For weight C: ( 85 , \text{lbs} \times 195 , \text{inches} = 16575 , \text{in-lbs} )

Now, sum the moments:

[ 2025 + 23985 + 16575 = 42585 , \text{in-lbs} ]