Given:
Mass of disc (m) = 100 gm = 0.1 kg
Mass of each bullet (m1) = 5 gm = 0.005 kg
Rate of firing bullets (n) = 10 bullets/s

To find:
Velocity of each bullet at the time of impact

Assumptions:
1. There is no external force acting on the system.
2. The bullets and the disc move in a horizontal plane.
3. There is no loss of kinetic energy during the collision between the bullets and the disc.

Explanation:
Step 1: Calculate the total momentum of the system before the bullets are fired.

Momentum (p) = mass (m) × velocity (v)

The velocity of the disc is not given, but as it is floating horizontally in air, we can assume it to be zero. Therefore, the initial momentum of the system before the bullets are fired is zero.

Step 2: Calculate the change in momentum of the system after the bullets are fired.

The mass and velocity of each bullet are given. Since the bullets rebound with the same speed in the opposite direction, the change in momentum of each bullet will be twice its initial momentum.

Change in momentum of each bullet (Δp1) = 2 × (mass of bullet) × (velocity of bullet)

Step 3: Calculate the rate of change of momentum of the system.

Rate of change of momentum (Δp) = (mass of bullet) × (rate of firing bullets)

Since the bullets are fired at a rate of 10 bullets/s and each bullet has a mass of 0.005 kg, the rate of change of momentum is:

Δp = (0.005 kg) × (10 bullets/s) = 0.05 kg·m/s

Step 4: Calculate the velocity of each bullet at the time of impact.

As per the law of conservation of momentum, the total change in momentum of the system is equal to the rate of change of momentum.

Total change in momentum of the system = Rate of change of momentum of the system

0.05 kg·m/s = 2 × (mass of bullet) × (velocity of bullet)

Substituting the values, we can solve for the velocity of each bullet:

0.05 kg·m/s = 2 × (0.005 kg) × (velocity of bullet)

Velocity of bullet = 0.05 kg·m/s / (2 × 0.005 kg) = 5 m/s

Therefore, the velocity of each bullet at the time of impact is 5 m/s.