To calculate the kinetic energy (KE) of the racehorse and its jockey, we 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:
- \( m = 512 \) 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:
\[ KE = \frac{1}{2} \times 512 , \text{kg} \times (18.8 , \text{m/s})^2 \]
First, calculate \( (18.8 , \text{m/s})^2 \):
\[ (18.8)^2 = 353.44 , \text{m}^2/\text{s}^2 \]
Now, substitute this back into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 512 \times 353.44 \]
Calculating \( \frac{1}{2} \times 512 \):
\[ \frac{1}{2} \times 512 = 256 \]
Now, multiply \( 256 \) by \( 353.44 \):
\[ KE = 256 \times 353.44 \approx 90404.16 \]
Therefore, the kinetic energy of the racehorse and its jockey is approximately \( 90404.16 \) joules.
Rounding to an appropriate precision, we can state:
\[ \boxed{90404 , \text{J}} \]
as the kinetic energy.