To determine which object is on the tallest hill, we need to calculate the height of each hill using the potential energy formula:
[tex]\[
E_p = m \cdot g \cdot h
\][/tex]
where [tex]\(E_p\)[/tex] is the potential energy, [tex]\(m\)[/tex] is the mass, [tex]\(g\)[/tex] is the acceleration due to gravity (9.8 m/s²), and [tex]\(h\)[/tex] is the height. We can rearrange this formula to solve for height [tex]\(h\)[/tex]:
[tex]\[
h = \frac{E_p}{m \cdot g}
\][/tex]
Let's calculate the height for each object step by step.
1. Object W:
[tex]\[
m = 50 \, \text{kg}, \, E_p = 980 \, \text{J}
\][/tex]
[tex]\[
h = \frac{980}{50 \times 9.8} = \frac{980}{490} \approx 2 \, \text{m}
\][/tex]
2. Object X:
[tex]\[
m = 35 \, \text{kg}, \, E_p = 1{,}029 \, \text{J}
\][/tex]
[tex]\[
h = \frac{1{,}029}{35 \times 9.8} = \frac{1{,}029}{343} \approx 3 \, \text{m}
\][/tex]
3. Object Y:
[tex]\[
m = 62 \, \text{kg}, \, E_p = 1{,}519 \, \text{J}
\][/tex]
[tex]\[
h = \frac{1{,}519}{62 \times 9.8} = \frac{1{,}519}{607.6} \approx 2.5 \, \text{m}
\][/tex]
4. Object Z:
[tex]\[
m = 24 \, \text{kg}, \, E_p = 1{,}176 \, \text{J}
\][/tex]
[tex]\[
h = \frac{1{,}176}{24 \times 9.8} = \frac{1{,}176}{235.2} \approx 5 \, \text{m}
\][/tex]
The calculated heights are:
- Object W: 2 meters
- Object X: 3 meters
- Object Y: 2.5 meters
- Object Z: 5 meters
From these calculations, we see that Object Z is on the tallest hill with a height of approximately 5 meters.
Thus, the answer is:
Z
