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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,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.
We are given:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
Our goal is to solve for the mass ([tex]\( m \)[/tex]). Rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[
m = \frac{PE}{g \times h}
\][/tex]
Substitute the given values into the formula:
[tex]\[
m = \frac{235,200}{9.8 \times 30}
\][/tex]
Now, calculate the denominator:
[tex]\[
9.8 \times 30 = 294
\][/tex]
Substitute back to solve for [tex]\( m \)[/tex]:
[tex]\[
m = \frac{235,200}{294}
\][/tex]
Upon performing the division, we find:
[tex]\[
m = 800
\][/tex]
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
So, the correct answer is [tex]\( \boxed{800 \, \text{kg}} \)[/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]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.
We are given:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
Our goal is to solve for the mass ([tex]\( m \)[/tex]). Rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[
m = \frac{PE}{g \times h}
\][/tex]
Substitute the given values into the formula:
[tex]\[
m = \frac{235,200}{9.8 \times 30}
\][/tex]
Now, calculate the denominator:
[tex]\[
9.8 \times 30 = 294
\][/tex]
Substitute back to solve for [tex]\( m \)[/tex]:
[tex]\[
m = \frac{235,200}{294}
\][/tex]
Upon performing the division, we find:
[tex]\[
m = 800
\][/tex]
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
So, the correct answer is [tex]\( \boxed{800 \, \text{kg}} \)[/tex].
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