Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy (235,200 Joules),
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.81 m/s² on Earth),
- [tex]\( h \)[/tex] is the height (30 meters).
We need to rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now we can plug in the values:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.81 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Calculating this gives us the mass:
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
Since the question is asking for the mass and provides multiple choices, we can see that the closest correct option is [tex]\( 800 \, \text{kg} \)[/tex]. Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy (235,200 Joules),
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.81 m/s² on Earth),
- [tex]\( h \)[/tex] is the height (30 meters).
We need to rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now we can plug in the values:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.81 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Calculating this gives us the mass:
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
Since the question is asking for the mass and provides multiple choices, we can see that the closest correct option is [tex]\( 800 \, \text{kg} \)[/tex]. Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex].
