To calculate the kinetic energy (KE) of the roller-coaster car and its passengers at the bottom of the hill, we can use the formula:
\[ KE = \frac{1}{2}mv^2 \]
where:
- \( m \) is the mass in kilograms (1,063 kg),
- \( v \) is the speed in meters per second (33 m/s).
Plugging in the values:
\[ KE = \frac{1}{2} \times 1,063 , \text{kg} \times (33 , \text{m/s})^2 \]
Calculating \( (33 , \text{m/s})^2 \):
\[ (33)^2 = 1,089 \]
Now substituting back into the equation:
\[ KE = \frac{1}{2} \times 1,063 \times 1,089 \]
Calculating the product:
\[ KE = \frac{1}{2} \times 1,156,407 , \text{kg m}^2/\text{s}^2 \]
\[ KE = 578,203.5 , \text{J} \]
Rounding that to match typical significant figures found in physics, we get:
\[ KE \approx 578,803.5 , \text{J} \]
Thus, the correct amount of kinetic energy at the bottom of the hill is:
578,803.5 J
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