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Answer :
To solve this problem, we need to find the mass of the roller coaster using the formula for potential energy (PE), which is given by:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy in joules.
- [tex]\( m \)[/tex] is the mass in kilograms.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex].
- [tex]\( h \)[/tex] is the height in meters.
We are 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 find the mass [tex]\( m \)[/tex]. To do this, we rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plugging the given values into the equation:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
When you calculate the above expression, you get:
[tex]\[ m \approx 799.18 \][/tex]
Since we need to choose from the given multiple-choice options, we round [tex]\( 799.18 \)[/tex] to the nearest whole number, which is [tex]\( 800 \)[/tex].
Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex], making the correct choice:
800 kg
[tex]\[ PE = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy in joules.
- [tex]\( m \)[/tex] is the mass in kilograms.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex].
- [tex]\( h \)[/tex] is the height in meters.
We are 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 find the mass [tex]\( m \)[/tex]. To do this, we rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plugging the given values into the equation:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
When you calculate the above expression, you get:
[tex]\[ m \approx 799.18 \][/tex]
Since we need to choose from the given multiple-choice options, we round [tex]\( 799.18 \)[/tex] to the nearest whole number, which is [tex]\( 800 \)[/tex].
Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex], making the correct choice:
800 kg
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