A rifle man, who together with his rifle has a mass of 100 kg, stands on a smooth surface and fires 10 shots horizontally. Each bullet has a mass 10 g and a muzzle velocity of 800 `ms^(-1)` . The velocity which the rifle man attains after firing 10 shots is

Options

A. `8ms^(-1)`
B. `0.8 ms^(-1)`
C. `0.08 ms^(-1)`
D. `-0.8 ms^(-1)`

Answer

To solve the problem, we can use the principle of conservation of momentum. When the rifleman fires the bullets, the momentum before firing must equal the momentum after firing.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the rifleman and rifle (M) = 100 kg
- Mass of each bullet (m) = 10 g = 0.01 kg (conversion from grams to kilograms)
- Muzzle velocity of each bullet (v) = 800 m/s
- Number of shots fired (n) = 10

2. **Calculate the Total Mass of Bullets Fired:**
\[ \text{Total mass of bullets} = n \times m = 10 \times 0.01 \, \text{kg} = 0.1 \, \text{kg} \]

3. **Calculate the Total Momentum of the Bullets:**
\[ \text{Total momentum of bullets} = \text{Total mass of bullets} \times \text{Muzzle velocity} = 0.1 \, \text{kg} \times 800 \, \text{m/s} = 80 \, \text{kg m/s} \]

4. **Apply Conservation of Momentum:**
Before firing, the total momentum of the system (rifleman + rifle + bullets) is zero since they are at rest. After firing, the momentum of the rifleman (R) moving backward must equal the momentum of the bullets moving forward:
\[ 0 = M \cdot V + \text{Total momentum of bullets} \]
where \( V \) is the velocity of the rifleman after firing.

5. **Set Up the Equation:**
\[ 0 = 100 \, \text{kg} \cdot V + 80 \, \text{kg m/s} \]
Rearranging gives:
\[ 100 \, \text{kg} \cdot V = -80 \, \text{kg m/s} \]

6. **Solve for the Velocity of the Rifleman:**
\[ V = \frac{-80 \, \text{kg m/s}}{100 \, \text{kg}} = -0.8 \, \text{m/s} \]
The negative sign indicates that the rifleman moves in the opposite direction to the bullets.

### Final Answer:
The velocity which the rifleman attains after firing 10 shots is \( 0.8 \, \text{m/s} \) in the opposite direction to the bullets.