To calculate the kinetic energy (KE) of the cannonball, we can use the kinetic energy formula:
\[ KE = \frac{1}{2} mv^2 \]
where:
- \( m \) is the mass of the object (in kg)
- \( v \) is the velocity of the object (in m/s)
Given:
- \( m = 7.00 , \text{kg} \)
- \( v = 75.0 , \text{m/s} \)
Substituting the values into the formula:
\[ KE = \frac{1}{2} \times 7.00 , \text{kg} \times (75.0 , \text{m/s})^2 \]
Calculating \( (75.0)^2 \):
\[ (75.0)^2 = 5625 , \text{m}^2/\text{s}^2 \]
Now, substituting that back into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 7.00 \times 5625 = 3.5 \times 5625 \]
Calculating \( 3.5 \times 5625 \):
\[ KE = 19687.5 , \text{J} \]
Rounding this to the nearest whole number gives:
\[ KE \approx 19,688 , \text{J} \]
The closest option provided is 19,700 J.
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