Answer :
To solve the problem of finding the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, given as 235,200 joules.
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 meters per second squared (m/s²).
- [tex]\( h \)[/tex] is the height of the hill, 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]
Substituting in the known values:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Now, calculate the product of [tex]\( 9.8 \times 30 \)[/tex]:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Then, divide the potential energy by this product to find the mass:
[tex]\[ m = \frac{235,200}{294} \][/tex]
After performing the division, the mass ([tex]\( m \)[/tex]) is found to be 800 kilograms.
Thus, the mass of the roller coaster is 800 kg. The correct answer is:
800 kg.
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, given as 235,200 joules.
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 meters per second squared (m/s²).
- [tex]\( h \)[/tex] is the height of the hill, 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]
Substituting in the known values:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Now, calculate the product of [tex]\( 9.8 \times 30 \)[/tex]:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Then, divide the potential energy by this product to find the mass:
[tex]\[ m = \frac{235,200}{294} \][/tex]
After performing the division, the mass ([tex]\( m \)[/tex]) is found to be 800 kilograms.
Thus, the mass of the roller coaster is 800 kg. The correct answer is:
800 kg.
