Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [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 of the hill, and
- PE is the given potential energy.
Given:
- [tex]\( \text{Potential Energy} = 235,200 \, \text{Joules} \)[/tex],
- [tex]\( h = 30 \, \text{meters} \)[/tex],
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex].
We need to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Substituting the given values:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
This value approximately equals 799.18 kg, which is not an exact match to any of the given options. So, the closest option to 799.18 kg seems to be 800 kg. Therefore, the mass of the roller coaster is approximately 800 kg.
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [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 of the hill, and
- PE is the given potential energy.
Given:
- [tex]\( \text{Potential Energy} = 235,200 \, \text{Joules} \)[/tex],
- [tex]\( h = 30 \, \text{meters} \)[/tex],
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex].
We need to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Substituting the given values:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
This value approximately equals 799.18 kg, which is not an exact match to any of the given options. So, the closest option to 799.18 kg seems to be 800 kg. Therefore, the mass of the roller coaster is approximately 800 kg.
