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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]\( 235,200 \, \text{Joules} \)[/tex].
- [tex]\( m \)[/tex] is the mass, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
- [tex]\( h \)[/tex] is the height, which is [tex]\( 30 \, \text{meters} \)[/tex].
Steps to solve for the mass [tex]\( m \)[/tex]:
1. Start by rearranging the formula to solve for mass:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
2. Substitute the known values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
3. Calculate the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
4. Divide the potential energy by the result from step 3:
[tex]\[ m = \frac{235,200}{294} \][/tex]
5. Compute the division to find the mass:
[tex]\[ m \approx 800 \][/tex]
Thus, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex]. Therefore, the correct answer is [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, which is [tex]\( 235,200 \, \text{Joules} \)[/tex].
- [tex]\( m \)[/tex] is the mass, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
- [tex]\( h \)[/tex] is the height, which is [tex]\( 30 \, \text{meters} \)[/tex].
Steps to solve for the mass [tex]\( m \)[/tex]:
1. Start by rearranging the formula to solve for mass:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
2. Substitute the known values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
3. Calculate the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
4. Divide the potential energy by the result from step 3:
[tex]\[ m = \frac{235,200}{294} \][/tex]
5. Compute the division to find the mass:
[tex]\[ m \approx 800 \][/tex]
Thus, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex]. Therefore, the correct answer is [tex]\( 800 \, \text{kg} \)[/tex].
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