To determine the total kinetic energy of the system, we need to calculate the kinetic energy of the cannonball and then add it to the kinetic energy of the cannon.
The formula for kinetic energy (KE) is given by:
\[ KE = \frac{1}{2} m v^2 \]
where \(m\) is the mass and \(v\) is the velocity.
- Calculate the kinetic energy of the cannonball:
The mass of the cannonball \(m = 18 , \text{kg}\) and the velocity \(v = 23 , \text{m/s}\).
\[ KE_{\text{cannonball}} = \frac{1}{2} \times (18) \times (23)^2 \]
Calculating \((23)^2\):
\[ 23^2 = 529 \]
Now substituting this value back:
\[ KE_{\text{cannonball}} = \frac{1}{2} \times 18 \times 529 = 9 \times 529 = 4761 , \text{J} \]
- Total kinetic energy of the system:
Now, we add the kinetic energy of the cannon to the kinetic energy of the cannonball.
Given that the kinetic energy of the cannon is \(72,000 , \text{J}\):
\[ KE_{\text{total}} = KE_{\text{cannon}} + KE_{\text{cannonball}} \] \[ KE_{\text{total}} = 72,000 , \text{J} + 4761 , \text{J} = 76,761 , \text{J} \]
Therefore, the total kinetic energy of the system is 76,761 J.
So the correct response is:
76,761 J