Answer :
To find the mass of the roller coaster, you can use the formula for potential energy:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy (given as 235,200 J),
- [tex]\( m \)[/tex] is the mass of the roller coaster (which we are solving for),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.81 m/s²),
- [tex]\( h \)[/tex] is the height (given as 30 m).
To solve for the mass [tex]\( m \)[/tex], we rearrange the formula:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plug in the given values:
[tex]\[ m = \frac{235,200}{9.81 \cdot 30} \][/tex]
Simplify the calculation:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \text{ kg} \][/tex]
Rounding this to the nearest whole number, the mass of the roller coaster is approximately 800 kg.
Therefore, the closest answer from the options provided is 800 kg.
[tex]\[ PE = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy (given as 235,200 J),
- [tex]\( m \)[/tex] is the mass of the roller coaster (which we are solving for),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.81 m/s²),
- [tex]\( h \)[/tex] is the height (given as 30 m).
To solve for the mass [tex]\( m \)[/tex], we rearrange the formula:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plug in the given values:
[tex]\[ m = \frac{235,200}{9.81 \cdot 30} \][/tex]
Simplify the calculation:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \text{ kg} \][/tex]
Rounding this to the nearest whole number, the mass of the roller coaster is approximately 800 kg.
Therefore, the closest answer from the options provided is 800 kg.
