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Answer :
To find the mass of the roller coaster, we can use the formula for potential energy, which is:
[tex]\[ PE = m \times g \times h \][/tex]
Here:
- [tex]\( PE \)[/tex] represents potential energy in joules,
- [tex]\( m \)[/tex] represents mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height in meters.
You are given:
- The potential energy ([tex]\( PE \)[/tex]) is [tex]\( 235,200 \)[/tex] joules,
- The height ([tex]\( h \)[/tex]) is [tex]\( 30 \)[/tex] meters.
To find the mass ([tex]\( m \)[/tex]), we need to rearrange the formula:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, let's plug in the values:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \][/tex]
The calculated mass is approximately [tex]\( 799.18 \, \text{kg} \)[/tex]. Based on the given options, the closest mass value is [tex]\( 800 \, \text{kg} \)[/tex].
Therefore, the mass of the roller coaster is most likely [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ PE = m \times g \times h \][/tex]
Here:
- [tex]\( PE \)[/tex] represents potential energy in joules,
- [tex]\( m \)[/tex] represents mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height in meters.
You are given:
- The potential energy ([tex]\( PE \)[/tex]) is [tex]\( 235,200 \)[/tex] joules,
- The height ([tex]\( h \)[/tex]) is [tex]\( 30 \)[/tex] meters.
To find the mass ([tex]\( m \)[/tex]), we need to rearrange the formula:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, let's plug in the values:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \][/tex]
The calculated mass is approximately [tex]\( 799.18 \, \text{kg} \)[/tex]. Based on the given options, the closest mass value is [tex]\( 800 \, \text{kg} \)[/tex].
Therefore, the mass of the roller coaster is most likely [tex]\( 800 \, \text{kg} \)[/tex].
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