Answer :
To determine 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.
- [tex]\( m \)[/tex] is the mass.
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]).
- [tex]\( h \)[/tex] is the height.
We know:
- The potential energy [tex]\( PE = 235,200 \, \text{Joules} \)[/tex].
- The height [tex]\( h = 30 \, \text{meters} \)[/tex].
- The acceleration due to gravity [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex].
We need to find the mass [tex]\( m \)[/tex]. Let's rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Plug in the given values:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
Calculate the denominator:
[tex]\[ 9.81 \times 30 = 294.3 \][/tex]
Now calculate the mass:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.184 \][/tex]
Therefore, the mass of the roller coaster is approximately [tex]\( 799.18 \, \text{kg} \)[/tex]. Based on the given options, the closest answer is [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ PE = m \times g \times h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy.
- [tex]\( m \)[/tex] is the mass.
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]).
- [tex]\( h \)[/tex] is the height.
We know:
- The potential energy [tex]\( PE = 235,200 \, \text{Joules} \)[/tex].
- The height [tex]\( h = 30 \, \text{meters} \)[/tex].
- The acceleration due to gravity [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex].
We need to find the mass [tex]\( m \)[/tex]. Let's rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Plug in the given values:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
Calculate the denominator:
[tex]\[ 9.81 \times 30 = 294.3 \][/tex]
Now calculate the mass:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.184 \][/tex]
Therefore, the mass of the roller coaster is approximately [tex]\( 799.18 \, \text{kg} \)[/tex]. Based on the given options, the closest answer is [tex]\( 800 \, \text{kg} \)[/tex].
