Answer :
To solve the problem of finding the mass of the roller coaster, we can use the formula for gravitational potential energy:
[tex]\[ PE = m \times g \times h \][/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 gravitational acceleration, usually approximated as 9.81 meters per second squared.
- [tex]\( h \)[/tex] is the height, given as 30 meters.
We need to solve for the mass ([tex]\( m \)[/tex]). Rearranging the formula to find [tex]\( m \)[/tex], we get:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, plug in the known values:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
Perform the multiplication in the denominator:
[tex]\[ g \times h = 9.81 \times 30 = 294.3 \][/tex]
Now, divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \][/tex]
The calculation gives us a mass of approximately 799.18 kilograms. Since this is closest to 800 kilograms in the options provided, the mass of the roller coaster is approximately:
800 kilograms
[tex]\[ PE = m \times g \times h \][/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 gravitational acceleration, usually approximated as 9.81 meters per second squared.
- [tex]\( h \)[/tex] is the height, given as 30 meters.
We need to solve for the mass ([tex]\( m \)[/tex]). Rearranging the formula to find [tex]\( m \)[/tex], we get:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, plug in the known values:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
Perform the multiplication in the denominator:
[tex]\[ g \times h = 9.81 \times 30 = 294.3 \][/tex]
Now, divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \][/tex]
The calculation gives us a mass of approximately 799.18 kilograms. Since this is closest to 800 kilograms in the options provided, the mass of the roller coaster is approximately:
800 kilograms
