To find the total kinetic energy of the system (cannon + cannonball), 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:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass and \( v \) is the velocity.
- Calculate the kinetic energy of the cannonball:
- Mass of the cannonball \( m = 18 , \text{kg} \)
- Velocity of the cannonball \( v = 23 , \text{m/s} \)
\[ KE_{\text{cannonball}} = \frac{1}{2} \times 18 , \text{kg} \times (23 , \text{m/s})^2 \]
\[ KE_{\text{cannonball}} = \frac{1}{2} \times 18 \times 529 \]
\[ KE_{\text{cannonball}} = 9 \times 529 = 4761 , \text{J} \]
- Now, add the kinetic energy of the cannonball to the kinetic energy of the cannon to get the total kinetic energy of the system:
\[ KE_{\text{total}} = KE_{\text{cannon}} + KE_{\text{cannonball}} \]
Given that \( KE_{\text{cannon}} = 72,000 , \text{J} \):
\[ KE_{\text{total}} = 72,000 , \text{J} + 4,761 , \text{J} = 76,761 , \text{J} \]
Therefore, the total kinetic energy of the system is 76,761 J.
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