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Answer :
To solve the problem of finding the mass of the roller coaster, we need to 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 235,200 Joules.
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we want to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 m/s[tex]\(^2\)[/tex].
- [tex]\( h \)[/tex] is the height, given as 30 meters.
In this problem, we want to solve for the mass [tex]\( m \)[/tex]. We can rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
When you calculate this, you will find that:
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is 800 kg. So, 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, given as 235,200 Joules.
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we want to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 m/s[tex]\(^2\)[/tex].
- [tex]\( h \)[/tex] is the height, given as 30 meters.
In this problem, we want to solve for the mass [tex]\( m \)[/tex]. We can rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
When you calculate this, you will find that:
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is 800 kg. So, the correct answer is 800 kg.
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