Question

An eagle that has a mass of 4.5 kg is spotted 5 m above a lake. It flies up to its nest in a tree at a height of 25 m.

How much gravitational potential energy did the eagle gain?

221 J
882 J
1103 J
1323 J

Answer 1

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**.