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Answer :
To determine the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy in joules (J),
- [tex]\( m \)[/tex] is the mass in kilograms (kg) that we want to find,
- [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 (m).
Given:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex]
We need to rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now substitute the known values into the equation:
1. Multiply gravity ([tex]\( g \)[/tex]) by height ([tex]\( h \)[/tex]):
[tex]\[ 9.81 \, \text{m/s}^2 \times 30 \, \text{m} = 294.3 \, \text{m}^2/\text{s}^2 \][/tex]
2. Divide the potential energy ([tex]\( PE \)[/tex]) by the result from step 1 to find the mass:
[tex]\[ \frac{235,200 \, \text{J}}{294.3 \, \text{m}^2/\text{s}^2} \approx 799.18 \, \text{kg} \][/tex]
Rounding to the nearest whole number, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex].
So, the correct answer from the given choices is [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy in joules (J),
- [tex]\( m \)[/tex] is the mass in kilograms (kg) that we want to find,
- [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 (m).
Given:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex]
We need to rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now substitute the known values into the equation:
1. Multiply gravity ([tex]\( g \)[/tex]) by height ([tex]\( h \)[/tex]):
[tex]\[ 9.81 \, \text{m/s}^2 \times 30 \, \text{m} = 294.3 \, \text{m}^2/\text{s}^2 \][/tex]
2. Divide the potential energy ([tex]\( PE \)[/tex]) by the result from step 1 to find the mass:
[tex]\[ \frac{235,200 \, \text{J}}{294.3 \, \text{m}^2/\text{s}^2} \approx 799.18 \, \text{kg} \][/tex]
Rounding to the nearest whole number, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex].
So, the correct answer from the given choices is [tex]\( 800 \, \text{kg} \)[/tex].
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