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Answer :
To find the mass of the roller coaster at the top of the hill, you can use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( \text{PE} \)[/tex] is the potential energy, given as 235,200 Joules.
- [tex]\( m \)[/tex] is the mass, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately 9.8 m/s².
- [tex]\( h \)[/tex] is the height, given as 30 meters.
We need to solve for the mass [tex]\( m \)[/tex]. Rearrange the formula to get:
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
Now, plug the given values into the equation:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
First, calculate the denominator:
[tex]\[ 9.8 \cdot 30 = 294 \][/tex]
Now, divide the potential energy by the result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is 800 kg.
So, the correct answer is 800 kg.
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( \text{PE} \)[/tex] is the potential energy, given as 235,200 Joules.
- [tex]\( m \)[/tex] is the mass, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately 9.8 m/s².
- [tex]\( h \)[/tex] is the height, given as 30 meters.
We need to solve for the mass [tex]\( m \)[/tex]. Rearrange the formula to get:
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
Now, plug the given values into the equation:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
First, calculate the denominator:
[tex]\[ 9.8 \cdot 30 = 294 \][/tex]
Now, divide the potential energy by the result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[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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