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Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy (235,200 Joules in this case),
- [tex]\( m \)[/tex] is the mass of the roller coaster (which we need to find),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height (30 meters).
We rearrange the formula to solve for mass [tex]\( m \)[/tex]:
[tex]\[
m = \frac{PE}{g \cdot h}
\][/tex]
Plugging in the given values:
[tex]\[
m = \frac{235,200}{9.81 \cdot 30}
\][/tex]
Calculating the denominator first:
[tex]\[
9.81 \cdot 30 = 294.3
\][/tex]
Now, divide the potential energy by this result:
[tex]\[
m = \frac{235,200}{294.3} \approx 799.18 \, \text{kg}
\][/tex]
The calculated mass is approximately [tex]\( 799.18 \, \text{kg} \)[/tex]. Comparing this with the given answer options:
- 800 kg
- 7,840 kg
- 8,000 kg
- 78,400 kg
The closest option to our calculated mass is [tex]\( 800 \, \text{kg} \)[/tex]. Therefore, the mass of the roller coaster is approximately [tex]\( \boxed{800 \, \text{kg}} \)[/tex].
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy (235,200 Joules in this case),
- [tex]\( m \)[/tex] is the mass of the roller coaster (which we need to find),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height (30 meters).
We rearrange the formula to solve for mass [tex]\( m \)[/tex]:
[tex]\[
m = \frac{PE}{g \cdot h}
\][/tex]
Plugging in the given values:
[tex]\[
m = \frac{235,200}{9.81 \cdot 30}
\][/tex]
Calculating the denominator first:
[tex]\[
9.81 \cdot 30 = 294.3
\][/tex]
Now, divide the potential energy by this result:
[tex]\[
m = \frac{235,200}{294.3} \approx 799.18 \, \text{kg}
\][/tex]
The calculated mass is approximately [tex]\( 799.18 \, \text{kg} \)[/tex]. Comparing this with the given answer options:
- 800 kg
- 7,840 kg
- 8,000 kg
- 78,400 kg
The closest option to our calculated mass is [tex]\( 800 \, \text{kg} \)[/tex]. Therefore, the mass of the roller coaster is approximately [tex]\( \boxed{800 \, \text{kg}} \)[/tex].
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