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Answer :
To determine the mass of the roller coaster at the top of the hill, we can use the formula for potential energy:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height of the hill.
Given:
- The potential energy ([tex]\( PE \)[/tex]) is [tex]\( 235,200 \, \text{Joules} \)[/tex],
- The height ([tex]\( h \)[/tex]) is [tex]\( 30 \, \text{meters} \)[/tex].
We need to solve for the mass ([tex]\( m \)[/tex]). We can rearrange the formula:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plug in the known values:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.81 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Now, calculate the expression:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \][/tex]
After calculating, the mass of the roller coaster is approximately [tex]\( 799.18 \, \text{kg} \)[/tex].
Since the available answer choices are in larger increments, the closest value to our calculated result is [tex]\( 800 \, \text{kg} \)[/tex].
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ PE = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height of the hill.
Given:
- The potential energy ([tex]\( PE \)[/tex]) is [tex]\( 235,200 \, \text{Joules} \)[/tex],
- The height ([tex]\( h \)[/tex]) is [tex]\( 30 \, \text{meters} \)[/tex].
We need to solve for the mass ([tex]\( m \)[/tex]). We can rearrange the formula:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plug in the known values:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.81 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Now, calculate the expression:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \][/tex]
After calculating, the mass of the roller coaster is approximately [tex]\( 799.18 \, \text{kg} \)[/tex].
Since the available answer choices are in larger increments, the closest value to our calculated result is [tex]\( 800 \, \text{kg} \)[/tex].
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
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