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Answer :
To find the mass of the roller coaster, we can use the formula for potential energy, which is given by:
[tex]\[ \text{PE} = m \times g \times h \][/tex]
where:
- [tex]\(\text{PE}\)[/tex] is the potential energy,
- [tex]\(m\)[/tex] is the mass,
- [tex]\(g\)[/tex] is the acceleration due to gravity (approximately [tex]\(9.81 \, \text{m/s}^2\)[/tex]), and
- [tex]\(h\)[/tex] is the height.
We are given:
- [tex]\(\text{PE} = 235,200 \, \text{Joules}\)[/tex],
- [tex]\(h = 30 \, \text{meters}\)[/tex], and
- [tex]\(g = 9.81 \, \text{m/s}^2\)[/tex].
We need to solve for the mass [tex]\(m\)[/tex]. Rearranging the formula to solve for [tex]\(m\)[/tex], we get:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Substituting the known values into the equation gives:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m \approx \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
Rounding to the nearest whole number, the mass of the roller coaster is approximately 800 kg. Therefore, the correct answer is 800 kg.
[tex]\[ \text{PE} = m \times g \times h \][/tex]
where:
- [tex]\(\text{PE}\)[/tex] is the potential energy,
- [tex]\(m\)[/tex] is the mass,
- [tex]\(g\)[/tex] is the acceleration due to gravity (approximately [tex]\(9.81 \, \text{m/s}^2\)[/tex]), and
- [tex]\(h\)[/tex] is the height.
We are given:
- [tex]\(\text{PE} = 235,200 \, \text{Joules}\)[/tex],
- [tex]\(h = 30 \, \text{meters}\)[/tex], and
- [tex]\(g = 9.81 \, \text{m/s}^2\)[/tex].
We need to solve for the mass [tex]\(m\)[/tex]. Rearranging the formula to solve for [tex]\(m\)[/tex], we get:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Substituting the known values into the equation gives:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m \approx \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
Rounding to the nearest whole number, the mass of the roller coaster is approximately 800 kg. Therefore, the correct answer is 800 kg.
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