Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, which is given as [tex]\( 235,200 \)[/tex] 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]\( 9.8 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height of the hill, given as [tex]\( 30 \)[/tex] meters.
We can rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, substitute the known values into the equation:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
Among the given options, the correct answer is 800 kg.
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, which is given as [tex]\( 235,200 \)[/tex] 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]\( 9.8 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height of the hill, given as [tex]\( 30 \)[/tex] meters.
We can rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, substitute the known values into the equation:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
Among the given options, the correct answer is 800 kg.
