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Answer :
To solve this problem, we need to find 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]\( PE \)[/tex] is the potential energy, which is given as 235,200 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, approximately 9.8 meters per second squared (m/s²).
- [tex]\( h \)[/tex] is the height of the hill, given as 30 meters.
We can rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, we plug in the given values:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
By calculating this, we find:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
So, the mass of the roller coaster is 800 kg. Therefore, the correct answer is 800 kg.
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, which is given as 235,200 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, approximately 9.8 meters per second squared (m/s²).
- [tex]\( h \)[/tex] is the height of the hill, given as 30 meters.
We can rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, we plug in the given values:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
By calculating this, we find:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
So, the mass of the roller coaster is 800 kg. Therefore, the correct answer is 800 kg.
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