Answer :
[tex]Given:\\m=84kg\\h_0=1500m\\h_1=3100m\\g=9,81 \frac{m}{s^2} \\\\Find:\\\Delta E_p=?\\\\Solution\\\\\Delta E_p=E_p_1-E_p_0\\\\E_p=mgh\\\\\Delta E_p=mgh_1-mgh_0=mgh(h_1-h_0)\\\\\Delta E_p=84kg\cdot 9,81 \frac{m}{s^2} (3100m-1500m)=1318464J[/tex]
The hiker's change in potential energy is [tex]\( 1330560 \, \text{J} \).[/tex]
The hiker's change in potential energy is given by the formula:
[tex]\[ \Delta PE = m \cdot g \cdot \Delta h \][/tex]
where [tex]\( \Delta PE \)[/tex] is the change in potential energy, [tex]m[/tex] is the mass of the hiker, [tex]g[/tex] is the acceleration due to gravity, and [tex]\( \Delta h \)[/tex] is the change in height.
Given:
- The mass of the hiker, [tex]m[/tex], is 84 kg.
- The acceleration due to gravity, [tex]g[/tex], is approximately [tex]\( 9.8 \, \text{m/s}^2 \).[/tex]
- The change in height, [tex]\( \Delta h \),[/tex] is the difference between the final elevation and the initial elevation, which is [tex]\( 3100 \, \text{m} - 1500 \, \text{m} = 1600 \, \text{m} \).[/tex]
Plugging in the values, we get:
[tex]\[ \Delta PE = 84 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 1600 \, \text{m} \][/tex]
[tex]\[ \Delta PE = 84 \cdot 9.8 \cdot 1600 \][/tex]
[tex]\[ \Delta PE = 1330560 \, \text{J} \][/tex]
