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 [tex]\( 235,200 \)[/tex] Joules in this case.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex].
- [tex]\( h \)[/tex] is the height, which is [tex]\( 30 \)[/tex] meters.
- [tex]\( m \)[/tex] is the mass, which we need to find.
We rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, substituting the values we have:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
Carrying out the division gives:
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
So the closest given option is [tex]\( 800 \, \text{kg} \)[/tex]. Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, which is [tex]\( 235,200 \)[/tex] Joules in this case.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex].
- [tex]\( h \)[/tex] is the height, which is [tex]\( 30 \)[/tex] meters.
- [tex]\( m \)[/tex] is the mass, which we need to find.
We rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, substituting the values we have:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
Carrying out the division gives:
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
So the closest given option is [tex]\( 800 \, \text{kg} \)[/tex]. Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex].
