To calculate the kinetic energy (KE) of the roller-coaster car 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 of the car and passengers (1,088 kg),
- \( v \) is the speed of the car at the bottom of the hill (33 m/s).
Plugging in the values:
\[ KE = \frac{1}{2} \times 1088 , \text{kg} \times (33 , \text{m/s})^2 \]
Calculating \( (33 , \text{m/s})^2 \):
\[ 33^2 = 1089 , \text{m}^2/\text{s}^2 \]
Now, substituting this back into the kinetic energy equation:
\[ KE = \frac{1}{2} \times 1088 \times 1089 \]
Calculating \( \frac{1}{2} \times 1088 = 544 \):
\[ KE = 544 \times 1089 \]
Now performing the multiplication:
\[ KE = 544 \times 1089 = 591,936 , \text{J} \]
However, I notice that none of the answer choices match this exactly. The closest round number calculation could be interpreted in terms of significant figures or rounding errors, so let's check again:
Calculating directly,
\[ 544 \times 1089 \approx 592,416 , \text{J} \]
So the kinetic energy of the car at the bottom of the hill is:
\[ \boxed{592,416 , \text{J}} \]
1 answer