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Answer :
To find the mass of the roller coaster, we can use the formula for potential energy, which is:
[tex]\[ \text{Potential Energy (PE)} = \text{mass (m)} \times \text{gravity (g)} \times \text{height (h)} \][/tex]
We know the following values:
- Potential Energy (PE) = 235,200 Joules
- Height (h) = 30 meters
- Gravity (g) = 9.81 m/s² (which is the standard acceleration due to gravity on Earth)
We need to rearrange the formula to solve for mass (m):
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Now, we can substitute the known values into the equation:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.81 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
After performing the calculation, we get:
[tex]\[ m \approx 799.18 \][/tex]
So, the mass of the roller coaster is approximately 799.18 kg. Rounding this to the nearest whole number gives us 800 kg. Therefore, the closest answer choice is 800 kg.
[tex]\[ \text{Potential Energy (PE)} = \text{mass (m)} \times \text{gravity (g)} \times \text{height (h)} \][/tex]
We know the following values:
- Potential Energy (PE) = 235,200 Joules
- Height (h) = 30 meters
- Gravity (g) = 9.81 m/s² (which is the standard acceleration due to gravity on Earth)
We need to rearrange the formula to solve for mass (m):
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Now, we can substitute the known values into the equation:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.81 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
After performing the calculation, we get:
[tex]\[ m \approx 799.18 \][/tex]
So, the mass of the roller coaster is approximately 799.18 kg. Rounding this to the nearest whole number gives us 800 kg. Therefore, the closest answer choice is 800 kg.
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