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, given as 235,200 Joules,
- [tex]\( m \)[/tex] is the mass (which we are trying to find),
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 m/s²,
- [tex]\( h \)[/tex] is the height, given as 30 meters.
We need to rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Calculating this, we get:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
So, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
Therefore, the correct answer is 800 kg.
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, given as 235,200 Joules,
- [tex]\( m \)[/tex] is the mass (which we are trying to find),
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 m/s²,
- [tex]\( h \)[/tex] is the height, given as 30 meters.
We need to rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Calculating this, we get:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
So, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
Therefore, the correct answer is 800 kg.
