Question

The power of a gun which fires 120 bullets per minute with a velocity 120 ms$^{-1}$ is: (given the mass of each bullet is 100 g)

• A. 86400 W
• B. 14.4 kW
• C. 1.44 kW
• D. 1220 W

Hint:

To calculate the power of a gun, determine the work done per bullet (kinetic energy) and then divide it by the time interval during which the bullets are fired.

Answer 1

The Correct Option is C

The power \( P \) of the gun can be calculated using the formula for the power delivered to the bullets: \[ P = \frac{\text{Work}}{\text{Time}} \] The work done per bullet is equal to the kinetic energy given by: \[ \text{Work per bullet} = \frac{1}{2} m v^2 \] Where: - \( m \) is the mass of each bullet, - \( v \) is the velocity of the bullet. Given: - \( m = 100 \, \text{g} = 0.1 \, \text{kg} \), - \( v = 120 \, \text{ms}^{-1} \), - The number of bullets fired per minute is 120, which means \( 120 \, \text{bullets} \) in \( 60 \, \text{seconds} \). Now, calculate the work done per bullet: \[ \text{Work per bullet} = \frac{1}{2} \times 0.1 \times 120^2 = 0.05 \times 14400 = 720 \, \text{J} \] Next, calculate the total work done in 60 seconds (since 120 bullets are fired in 1 minute): \[ \text{Total work} = 120 \times 720 = 86400 \, \text{J} \] Now, calculate the power: \[ P = \frac{86400}{60} = 1440 \, \text{W} = 1.44 \, \text{kW} \] Thus, the power of the gun is \( 1.44 \, \text{kW} \).