To calculate the potential energy (PE) of the roller coaster car at the top of the hill, we can use the formula for gravitational potential energy:
\[ PE = mgh \]
where:
- \( m \) is the mass (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height (in meters).
Given:
- \( m = 1088 , \text{kg} \)
- \( h = 62 , \text{m} \)
- \( g = 9.81 , \text{m/s}^2 \)
We can now plug in the values:
\[ PE = 1088 , \text{kg} \times 9.81 , \text{m/s}^2 \times 62 , \text{m} \]
Calculating step-by-step:
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Calculate \( 9.81 \times 62 \): \[ 9.81 \times 62 = 609.42 , \text{m}^2/\text{s}^2 \]
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Now multiply by the mass: \[ PE = 1088 , \text{kg} \times 609.42 , \text{m}^2/\text{s}^2 = 663,125.76 , \text{J} \]
So, the potential energy of the roller coaster car at the top of the hill is approximately:
\[ PE \approx 663,126 , \text{J} \quad \text{(rounded to the nearest joule)} \]
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