To determine the kinetic energy of the roller coaster, we can follow these steps:
1. Recall the formula for kinetic energy:
[tex]\[
KE = \frac{1}{2} m v^2
\][/tex]
where [tex]\( KE \)[/tex] is the kinetic energy, [tex]\( m \)[/tex] is the mass, and [tex]\( v \)[/tex] is the velocity.
2. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 620.0 kg
- Velocity ([tex]\( v \)[/tex]) = 9.00 m/s
3. Substitute the given values into the kinetic energy formula:
[tex]\[
KE = \frac{1}{2} \times 620.0 \, \text{kg} \times (9.00 \, \text{m/s})^2
\][/tex]
4. Calculate the velocity squared:
[tex]\[
(9.00 \, \text{m/s})^2 = 81.00 \, \text{m}^2/\text{s}^2
\][/tex]
5. Multiply the mass by the squared velocity:
[tex]\[
620.0 \, \text{kg} \times 81.00 \, \text{m}^2/\text{s}^2 = 50,220 \, \text{kg} \cdot \text{m}^2/\text{s}^2
\][/tex]
6. Multiply by [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[
KE = \frac{1}{2} \times 50,220 \, \text{kg} \cdot \text{m}^2/\text{s}^2 = 25,110 \, \text{kg} \cdot \text{m}^2/\text{s}^2
\][/tex]
7. Round the final answer to 3 significant figures:
[tex]\[
KE = 25,100 \, \text{J}
\][/tex]
Thus, the kinetic energy of the roller coaster is [tex]\( 25,100 \, \text{J} \)[/tex]. The correct answer is:
[tex]\[ \boxed{25,100 \, \text{J}} \][/tex]
