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Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy in joules,
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height in meters.
Given:
- [tex]\(\text{PE} = 235,200 \, \text{Joules}\)[/tex]
- [tex]\( h = 30 \, \text{meters} \)[/tex]
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex]
We want to solve for [tex]\( m \)[/tex], so we rearrange the formula:
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
Substitute the given values into the formula:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m = 799.1845056065239 \][/tex]
The mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex].
Therefore, the correct answer is [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy in joules,
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height in meters.
Given:
- [tex]\(\text{PE} = 235,200 \, \text{Joules}\)[/tex]
- [tex]\( h = 30 \, \text{meters} \)[/tex]
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex]
We want to solve for [tex]\( m \)[/tex], so we rearrange the formula:
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
Substitute the given values into the formula:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m = 799.1845056065239 \][/tex]
The mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex].
Therefore, the correct answer is [tex]\( 800 \, \text{kg} \)[/tex].
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