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Answer :
To determine the mass of the roller coaster, we can use the formula for potential energy, which is:
[tex]\[ \text{PE} = m \times g \times h \][/tex]
where:
- [tex]\(\text{PE}\)[/tex] is the potential energy in joules (J),
- [tex]\(m\)[/tex] is the mass in kilograms (kg),
- [tex]\(g\)[/tex] is the acceleration due to gravity, which is approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex],
- [tex]\(h\)[/tex] is the height in meters (m).
Given:
- [tex]\(\text{PE} = 235,200 \, \text{J}\)[/tex]
- [tex]\(h = 30 \, \text{m}\)[/tex]
- [tex]\(g = 9.8 \, \text{m/s}^2\)[/tex]
We need to find the mass [tex]\(m\)[/tex]. We can rearrange the formula to solve for [tex]\(m\)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is 800 kg. The correct answer is [tex]\(800 \, \text{kg}\)[/tex].
[tex]\[ \text{PE} = m \times g \times h \][/tex]
where:
- [tex]\(\text{PE}\)[/tex] is the potential energy in joules (J),
- [tex]\(m\)[/tex] is the mass in kilograms (kg),
- [tex]\(g\)[/tex] is the acceleration due to gravity, which is approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex],
- [tex]\(h\)[/tex] is the height in meters (m).
Given:
- [tex]\(\text{PE} = 235,200 \, \text{J}\)[/tex]
- [tex]\(h = 30 \, \text{m}\)[/tex]
- [tex]\(g = 9.8 \, \text{m/s}^2\)[/tex]
We need to find the mass [tex]\(m\)[/tex]. We can rearrange the formula to solve for [tex]\(m\)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is 800 kg. The correct answer is [tex]\(800 \, \text{kg}\)[/tex].
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