To calculate the kinetic energy (KE) of the horse and jockey, we can use 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 the mass \( m = 520 \) kg and the velocity \( v = 18.8 \) m/s, we can plug these values into the formula:
\[ KE = \frac{1}{2} \times 520 , \text{kg} \times (18.8 , \text{m/s})^2 \]
Calculating \( (18.8 , \text{m/s})^2 \):
\[ (18.8)^2 = 353.44 , \text{m}^2/\text{s}^2 \]
Now substitute this back into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 520 , \text{kg} \times 353.44 , \text{m}^2/\text{s}^2 \]
Now calculate \( \frac{1}{2} \times 520 = 260 \):
\[ KE = 260 , \text{kg} \times 353.44 , \text{m}^2/\text{s}^2 \]
Calculating the final multiplication:
\[ KE = 92,894.4 , \text{J} \]
Thus, the kinetic energy of the horse and jockey is approximately:
\[ \boxed{91,894.4 , \text{J}} \]
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