To find the kinetic energy of the roller coaster car at the bottom of the hill, we can use the formula for kinetic energy (KE):
\[ KE = \frac{1}{2} m v^2 \]
where:
- \( m \) is the mass of the car and passengers, and
- \( v \) is the velocity of the car at the bottom of the hill.
Given:
- Mass, \( m = 1,088 \) kg
- Velocity, \( v = 33 \) m/s
Now, we can substitute the values into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 1,088 , \text{kg} \times (33 , \text{m/s})^2 \]
Calculating \( (33 , \text{m/s})^2 \):
\[ (33)^2 = 1,089 , \text{m}^2/\text{s}^2 \]
Now substitute back into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 1,088 , \text{kg} \times 1,089 , \text{m}^2/\text{s}^2 \]
Calculating \( \frac{1}{2} \times 1,088 \):
\[ \frac{1}{2} \times 1,088 = 544 , \text{kg} \]
Now multiply:
\[ KE = 544 , \text{kg} \times 1,089 , \text{m}^2/\text{s}^2 \]
Calculating the final result:
\[ KE = 592,176 , \text{kg m}^2/\text{s}^2 = 592,176 , \text{J} \]
Therefore, the kinetic energy of the car at the bottom of the hill is approximately:
\[ \boxed{592,176 , \text{J}} \]