To calculate the potential energy (PE) of the roller-coaster car at the top of the hill, we can use the formula:
\[ PE = mgh \]
where:
- \( m \) = mass (in kilograms) = 1,088 kg
- \( g \) = acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \))
- \( h \) = height (in meters) = 62 m
Now, let's plug in the values:
\[ PE = 1,088 , \text{kg} \times 9.81 , \text{m/s}^2 \times 62 , \text{m} \]
Now calculate it step-by-step:
-
Calculate \( g \times h \): \[ 9.81 , \text{m/s}^2 \times 62 , \text{m} = 609.42 , \text{m}^2/\text{s}^2 \]
-
Now calculate \( PE \): \[ PE = 1,088 , \text{kg} \times 609.42 , \text{m}^2/\text{s}^2 \approx 663,153.76 , \text{J} \]
Thus, rounding to the nearest whole number gives approximately 663,154 J. However, out of the options provided, it seems the closest match is:
661,068.8 J
So the answer is:
661,068.8 J