To calculate the kinetic energy (KE) of the cannonball, you can use the kinetic energy formula:
\[ KE = \frac{1}{2} m v^2 \]
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 \( (75.0 , \text{m/s})^2 \):
\[ 75.0^2 = 5625 , \text{m}^2/\text{s}^2 \]
Now substituting this back into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 7.00 , \text{kg} \times 5625 , \text{m}^2/\text{s}^2 \]
Calculating:
\[ KE = \frac{1}{2} \times 7.00 \times 5625 = 3.5 \times 5625 = 19687.5 , \text{J} \]
Rounding to the appropriate significant figures, it is approximately:
\[ KE \approx 19700 , \text{J} \]
So the answer is:
19,700 J.