Answer :
To find the change in Xanaxa's gravitational potential energy during her pursuit, we need to consider her movement from the ground up to the top of the building and then down to the bottom of the excavation. Let's go through the steps one-by-one:
1. Understanding Gravitational Potential Energy (GPE):
The formula to calculate gravitational potential energy is:
[tex]\[
U = m \cdot g \cdot h
\][/tex]
where [tex]\( U \)[/tex] is the gravitational potential energy, [tex]\( m \)[/tex] is the mass, [tex]\( g \)[/tex] is the gravitational acceleration (9.81 m/s²), and [tex]\( h \)[/tex] is the height.
2. Calculate GPE at the Top of the Building:
- Mass of Xanaxa, [tex]\( m = 62.7 \)[/tex] kg
- Height of the building, [tex]\( h = 197 \)[/tex] m
The GPE at the top is:
[tex]\[
U_{\text{top}} = 62.7 \cdot 9.81 \cdot 197 = 121172.14 \, \text{Joules}
\][/tex]
3. Calculate GPE at the Bottom of the Excavation:
- Note that since the excavation is below the ground level, the height [tex]\( h = -15.1 \)[/tex] m
The GPE at the bottom is:
[tex]\[
U_{\text{bottom}} = 62.7 \cdot 9.81 \cdot (-15.1) = -9287.81 \, \text{Joules}
\][/tex]
4. Determine the Change in Gravitational Potential Energy:
To find the change in gravitational potential energy ([tex]\( \Delta U \)[/tex]), subtract the GPE at the top of the building from the GPE at the bottom of the excavation:
[tex]\[
\Delta U = U_{\text{bottom}} - U_{\text{top}} = -9287.81 - 121172.14 = -130459.95 \, \text{Joules}
\][/tex]
Therefore, the magnitude of the change in Xanaxa's gravitational potential energy is [tex]\( 130,459.95 \)[/tex] Joules.
1. Understanding Gravitational Potential Energy (GPE):
The formula to calculate gravitational potential energy is:
[tex]\[
U = m \cdot g \cdot h
\][/tex]
where [tex]\( U \)[/tex] is the gravitational potential energy, [tex]\( m \)[/tex] is the mass, [tex]\( g \)[/tex] is the gravitational acceleration (9.81 m/s²), and [tex]\( h \)[/tex] is the height.
2. Calculate GPE at the Top of the Building:
- Mass of Xanaxa, [tex]\( m = 62.7 \)[/tex] kg
- Height of the building, [tex]\( h = 197 \)[/tex] m
The GPE at the top is:
[tex]\[
U_{\text{top}} = 62.7 \cdot 9.81 \cdot 197 = 121172.14 \, \text{Joules}
\][/tex]
3. Calculate GPE at the Bottom of the Excavation:
- Note that since the excavation is below the ground level, the height [tex]\( h = -15.1 \)[/tex] m
The GPE at the bottom is:
[tex]\[
U_{\text{bottom}} = 62.7 \cdot 9.81 \cdot (-15.1) = -9287.81 \, \text{Joules}
\][/tex]
4. Determine the Change in Gravitational Potential Energy:
To find the change in gravitational potential energy ([tex]\( \Delta U \)[/tex]), subtract the GPE at the top of the building from the GPE at the bottom of the excavation:
[tex]\[
\Delta U = U_{\text{bottom}} - U_{\text{top}} = -9287.81 - 121172.14 = -130459.95 \, \text{Joules}
\][/tex]
Therefore, the magnitude of the change in Xanaxa's gravitational potential energy is [tex]\( 130,459.95 \)[/tex] Joules.
