In a closed system consisting of a cannon and a cannonball, the kinetic energy of a cannon is 72,000 J. If the cannonball is 18 kg and has a velocity of 23 m/s when fired from the cannon, what is the total kinetic energy of the system?(1 point)

Question

Responses

71,793 J
71,793 J

76,761 J
76,761 J

72,207 J
72,207 J

67,239 J
67,239 J

Answer 1

To find 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.

1. Calculate the kinetic energy of the cannonball using the formula: \[ KE = \frac{1}{2}mv^2 \] where:

   • \( m \) = mass of the cannonball = 18 kg
   • \( v \) = velocity of the cannonball = 23 m/s

   \[ KE_{cannonball} = \frac{1}{2} \times 18 , \text{kg} \times (23 , \text{m/s})^2 \] \[ KE_{cannonball} = \frac{1}{2} \times 18 \times 529 \] \[ KE_{cannonball} = 9 \times 529 = 4761 , \text{J} \]

2. Add the kinetic energy of the cannon to the kinetic energy of the cannonball: \[ KE_{total} = KE_{cannon} + KE_{cannonball} \] \[ KE_{total} = 72000 , \text{J} + 4761 , \text{J} \] \[ KE_{total} = 76761 , \text{J} \]

The total kinetic energy of the system is 76,761 J.

Thus, the correct response is: 76,761 J.