Answer :
To find the mass of the roller coaster, we can use the formula for potential energy (PE), which is:
[tex]\[ PE = m \times g \times h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy, which is 235,200 Joules.
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we're trying to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 9.8 meters per second squared (m/s²).
- [tex]\( h \)[/tex] is the height of the hill, which is 30 meters.
We'll rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, plug in the values:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Calculate [tex]\( g \times h \)[/tex]:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Now divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m \approx 800 \][/tex]
So, the mass of the roller coaster is 800 kg. This matches the answer choice of 800 kg.
[tex]\[ PE = m \times g \times h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy, which is 235,200 Joules.
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we're trying to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is 9.8 meters per second squared (m/s²).
- [tex]\( h \)[/tex] is the height of the hill, which is 30 meters.
We'll rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, plug in the values:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Calculate [tex]\( g \times h \)[/tex]:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Now divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m \approx 800 \][/tex]
So, the mass of the roller coaster is 800 kg. This matches the answer choice of 800 kg.
