The kinetic energy (KE) can be calculated using the formula:
\[ KE = \frac{1}{2} m v^2 \]
where:
- \( m \) is the mass in kilograms,
- \( v \) is the velocity in meters per second.
Given:
- \( m = 512 \) kg (mass of the horse and jockey),
- \( v = 18.8 \) m/s (velocity of the horse).
Now, we can substitute the values into the formula:
\[ KE = \frac{1}{2} \times 512 , \text{kg} \times (18.8 , \text{m/s})^2 \]
Calculating \( (18.8 , \text{m/s})^2 \):
\[ (18.8)^2 = 353.44 , \text{m}^2/\text{s}^2 \]
Now, plugging it back into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 512 \times 353.44 \]
Calculating:
\[ KE = 256 \times 353.44 = 90,480.64 , \text{J} \]
Rounding this to one decimal place gives:
\[ KE \approx 90,480.6 , \text{J} \]
Thus, the kinetic energy of the horse and its jockey is approximately 90,480.6 J.