Answer :
To solve the problem, we need to determine the mass of the roller coaster using the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy, given as [tex]\( 235,200 \, J \)[/tex] (joules).
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we need to find.
- [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, given as [tex]\( 30 \, m \)[/tex] (meters).
Rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Substitute the given values into the equation:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
Calculate [tex]\( g \times h \)[/tex]:
[tex]\[ g \times h = 9.81 \times 30 = 294.3 \][/tex]
Now, substitute back to find [tex]\( m \)[/tex]:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
When you calculate this, you get approximately:
[tex]\[ m \approx 799.18 \, kg \][/tex]
The closest mass option to this result is [tex]\( 800 \, kg \)[/tex].
Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, kg \)[/tex].
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy, given as [tex]\( 235,200 \, J \)[/tex] (joules).
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we need to find.
- [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, given as [tex]\( 30 \, m \)[/tex] (meters).
Rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Substitute the given values into the equation:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
Calculate [tex]\( g \times h \)[/tex]:
[tex]\[ g \times h = 9.81 \times 30 = 294.3 \][/tex]
Now, substitute back to find [tex]\( m \)[/tex]:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
When you calculate this, you get approximately:
[tex]\[ m \approx 799.18 \, kg \][/tex]
The closest mass option to this result is [tex]\( 800 \, kg \)[/tex].
Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, kg \)[/tex].
