Answer :
To find the mass of the roller coaster, we need to use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]
In this formula:
- [tex]\( \text{PE} \)[/tex] is the potential energy, given as 235,200 J (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 [tex]\( 9.81 \, \text{m/s}^2 \)[/tex].
- [tex]\( h \)[/tex] is the height of the hill, given as 30 m.
Our goal is to solve for the mass [tex]\( m \)[/tex]. We can rearrange the formula to solve for [tex]\( m \)[/tex] as follows:
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
Let's plug in the given values:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.81 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Now, calculate the value:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m \approx 799.184 \][/tex]
Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex].
So, the correct answer is 800 kg.
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]
In this formula:
- [tex]\( \text{PE} \)[/tex] is the potential energy, given as 235,200 J (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 [tex]\( 9.81 \, \text{m/s}^2 \)[/tex].
- [tex]\( h \)[/tex] is the height of the hill, given as 30 m.
Our goal is to solve for the mass [tex]\( m \)[/tex]. We can rearrange the formula to solve for [tex]\( m \)[/tex] as follows:
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
Let's plug in the given values:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.81 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Now, calculate the value:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m \approx 799.184 \][/tex]
Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex].
So, the correct answer is 800 kg.
