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Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, which is given as 235,200 joules.
- [tex]\( m \)[/tex] is the mass of the object, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 meters per second squared.
- [tex]\( h \)[/tex] is the height, given as 30 meters.
We need to rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plug in the given values:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
Calculate the denominator:
[tex]\[ 9.8 \cdot 30 = 294 \][/tex]
Now divide the potential energy by this product:
[tex]\[ m = \frac{235,200}{294} \][/tex]
When you perform the division, you get:
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is 800 kg. The correct answer is 800 kg.
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, which is given as 235,200 joules.
- [tex]\( m \)[/tex] is the mass of the object, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 meters per second squared.
- [tex]\( h \)[/tex] is the height, given as 30 meters.
We need to rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plug in the given values:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
Calculate the denominator:
[tex]\[ 9.8 \cdot 30 = 294 \][/tex]
Now divide the potential energy by this product:
[tex]\[ m = \frac{235,200}{294} \][/tex]
When you perform the division, you get:
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is 800 kg. The correct answer is 800 kg.
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