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 (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height of the hill.
We're given:
- Potential Energy ([tex]\( \text{PE} \)[/tex]) = 235,200 Joules,
- Height ([tex]\( h \)[/tex]) = 30 meters.
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, plug in the given values:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
By computing this, we get:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is 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 (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height of the hill.
We're given:
- Potential Energy ([tex]\( \text{PE} \)[/tex]) = 235,200 Joules,
- Height ([tex]\( h \)[/tex]) = 30 meters.
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, plug in the given values:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
By computing this, we get:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is 800 kg.
