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