Given:
- Time taken to fire 30 bullets = 10s
- Velocity of each bullet = 500 m/s
- Mass of each bullet = 100g = 0.1kg

To Find:
- Power developed by the gun

Formula:
Power (P) = Work done (W) / Time taken (t)

Explanation:
1. First, let's calculate the total work done by the gun. Work is equal to the change in kinetic energy of the bullets.
- The initial kinetic energy of each bullet is zero (since they start from rest).
- The final kinetic energy of each bullet can be calculated using the formula: KE = (1/2)mv^2, where m is the mass and v is the velocity.
- The change in kinetic energy is: ΔKE = KE_final - KE_initial = (1/2)mv^2 - 0 = (1/2)mv^2.
- The total work done by the gun is given by: W = ΔKE * Number of bullets = (1/2)mv^2 * Number of bullets.

2. Next, let's calculate the power developed by the gun using the formula mentioned above.
- Power (P) = W / t, where W is the work done and t is the time taken.

Calculation:
1. Work done by the gun:
- ΔKE = (1/2)mv^2 = (1/2)(0.1kg)(500 m/s)^2 = 1250 J (joules)
- Number of bullets = 30
- W = ΔKE * Number of bullets = 1250 J * 30 = 37500 J (joules)

2. Power developed by the gun:
- P = W / t = 37500 J / 10s = 3750 W (watts)

Answer:
The power developed by the machine gun is 3750 watts.