To calculate the gravitational potential energy (GPE) gained by the eagle, we can use the formula:
\[ \text{GPE} = m \cdot g \cdot h \]
where:
- \( m \) is the mass of the eagle (4.5 kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the change in height.
First, we need to determine the change in height (\( h \)):
- The eagle starts at a height of 5 m and flies up to 25 m.
- Therefore, the change in height is: \[ h = 25 , \text{m} - 5 , \text{m} = 20 , \text{m} \]
Now, substitute the values into the GPE formula:
\[ \text{GPE} = 4.5 , \text{kg} \cdot 9.81 , \text{m/s}^2 \cdot 20 , \text{m} \]
Calculating it:
\[ \text{GPE} = 4.5 \cdot 9.81 \cdot 20 \] \[ \text{GPE} = 4.5 \cdot 196.2 \] \[ \text{GPE} = 882.9 , \text{J} \]
Rounding it to the nearest whole number, the eagle gains approximately:
\[ \text{GPE} \approx 882 , \text{J} \]
Thus, the correct answer is 882 J.
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