To calculate the kinetic energy (KE) of the racehorse and its jockey, you can use the formula:
\[ KE = \frac{1}{2} mv^2 \]
Where:
- \( m \) is the mass (in kilograms),
- \( v \) is the velocity (in meters per second).
Given:
- Mass \( m = 512 \) kg
- Velocity \( v = 18.8 \) m/s
Now, substituting the values into the formula:
\[ KE = \frac{1}{2} \times 512 , \text{kg} \times (18.8 , \text{m/s})^2 \]
First, calculate \( (18.8 , \text{m/s})^2 \):
\[ (18.8 , \text{m/s})^2 = 353.44 , \text{m}^2/\text{s}^2 \]
Now, substitute this back into the kinetic energy equation:
\[ KE = \frac{1}{2} \times 512 , \text{kg} \times 353.44 , \text{m}^2/\text{s}^2 \] \[ KE = 256 , \text{kg} \times 353.44 , \text{m}^2/\text{s}^2 \] \[ KE = 90,480.64 , \text{J} \]
Rounding this, the kinetic energy is approximately:
\[ KE \approx 90,480.6 , \text{J} \]
Thus, the correct answer is:
90,480.6 J