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Answer :
To find the mass of the roller coaster, you can use the formula for potential energy, which is:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( m \)[/tex] is the 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.
We are given:
- Potential Energy (PE) = 235,200 J (joules),
- Height (h) = 30 m,
- Gravity (g) = 9.81 m/s².
We need to find the mass [tex]\( m \)[/tex]. To do that, rearrange the formula to solve for mass:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Now, substitute the given values into the equation:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.81 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
[tex]\[ m \approx \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \][/tex]
Since we're looking for the closest answer from the given options, we round the calculated mass to the nearest whole number:
[tex]\[ m \approx 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is approximately 800 kg.
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( m \)[/tex] is the 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.
We are given:
- Potential Energy (PE) = 235,200 J (joules),
- Height (h) = 30 m,
- Gravity (g) = 9.81 m/s².
We need to find the mass [tex]\( m \)[/tex]. To do that, rearrange the formula to solve for mass:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Now, substitute the given values into the equation:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.81 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
[tex]\[ m \approx \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \][/tex]
Since we're looking for the closest answer from the given options, we round the calculated mass to the nearest whole number:
[tex]\[ m \approx 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is approximately 800 kg.
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