Answer :
To find the mass of the roller coaster at the top of the hill, we can use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, given as [tex]\( 235,200 \, \text{Joules} \)[/tex],
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex] on Earth,
- [tex]\( h \)[/tex] is the height of the hill, given as [tex]\( 30 \, \text{meters} \)[/tex],
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we need to find.
To find the mass [tex]\( m \)[/tex], we need to rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Now, let's plug in the given values:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
This calculation gives us:
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is [tex]\( \boxed{800 \, \text{kg}} \)[/tex].
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, given as [tex]\( 235,200 \, \text{Joules} \)[/tex],
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex] on Earth,
- [tex]\( h \)[/tex] is the height of the hill, given as [tex]\( 30 \, \text{meters} \)[/tex],
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we need to find.
To find the mass [tex]\( m \)[/tex], we need to rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Now, let's plug in the given values:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
This calculation gives us:
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is [tex]\( \boxed{800 \, \text{kg}} \)[/tex].
