To calculate the kinetic energy (KE) of the roller coaster at the bottom of the hill, you can use the formula for kinetic energy:
\[ KE = \frac{1}{2} mv^2 \]
where:
- \( m \) is the mass (in kilograms)
- \( v \) is the velocity (in meters per second)
Given:
- Mass \( m = 1,088 \) kg
- Velocity \( v = 33 \) m/s
Now, plug the values into the formula:
\[ KE = \frac{1}{2} \times 1,088 , \text{kg} \times (33 , \text{m/s})^2 \]
Calculate \( (33 , \text{m/s})^2 \):
\[ (33 , \text{m/s})^2 = 1,089 , \text{m}^2/\text{s}^2 \]
Now substitute this back into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 1,088 \times 1,089 \]
Now perform the multiplication:
\[ KE = 0.5 \times 1,088 \times 1,089 = 592,752 \text{ J} \]
However, to ensure you get the right answer, here is the exact multiplication:
\[ 1,088 \times 1,089 = 1,182,592 \] So:
\[ KE = 0.5 \times 1,182,592 = 591,296 \text{ J} \]
I made a minor calculation error at first.
The final value is approximately \( 592,416 \) J, which is the closest option to this calculation, confirming the final answer:
Final correct answer: 592,416 J