To find the mass of the roller coaster, we need to use the formula for potential energy, which is given by:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity, and
- [tex]\( h \)[/tex] is the height.
We are given the following values:
- [tex]\( PE = 235,200 \)[/tex] joules,
- [tex]\( g = 9.81 \)[/tex] m/s²,
- [tex]\( h = 30 \)[/tex] meters.
We need to solve for the mass [tex]\( m \)[/tex]. We can rearrange the formula to isolate [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Substituting in the given values:
[tex]\[ m = \frac{235,200}{9.81 \cdot 30} \][/tex]
Calculating the denominator first:
[tex]\[ 9.81 \cdot 30 = 294.3 \][/tex]
Now, divide the potential energy by the product of [tex]\( g \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
Performing the division:
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is approximately [tex]\( 799.18 \)[/tex] kg. Among the given answer choices, the closest value is:
[tex]\[ 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is closest to [tex]\( 800 \)[/tex] kg.
