To find the potential energy (PE) of the roller-coaster car at the top of the hill, we can use the formula:
\[ PE = mgh \]
where:
- \(m\) is the mass in kilograms (1,088 kg),
- \(g\) is the acceleration due to gravity (approximately \(9.8 , \text{m/s}^2\)),
- \(h\) is the height in meters (62 m).
Now, substituting the values into the formula:
\[ PE = 1,088 , \text{kg} \times 9.8 , \text{m/s}^2 \times 62 , \text{m} \]
Calculating step by step:
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Calculate \(g \times h\): \[ 9.8 , \text{m/s}^2 \times 62 , \text{m} = 607.6 , \text{m}^2/\text{s}^2 \]
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Now multiply by the mass \(m\): \[ PE = 1,088 , \text{kg} \times 607.6 , \text{m}^2/\text{s}^2 \] \[ PE = 661,068.8 , \text{J} \]
Thus, the potential energy of the roller-coaster car at the top of the hill is 661,068.8 J.
The correct answer from the provided options is 661,068.8 J.