Two perfectly elastic particles `A` and `B` of equal masses travelling along a line joining them with velocities `15 m//s` and `10m//s` respectively collide. Their velocities after the elastic collision will be (in m/s) respectively

Options

A. 0, 25
B. 3, 20
C. 10, 15
D. 20, 5

Answer

To solve the problem of finding the velocities of two perfectly elastic particles A and B after they collide, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Mass of particle A (m_A) = m (let's assume mass = m for simplicity)
- Mass of particle B (m_B) = m
- Initial velocity of particle A (u_A) = 15 m/s
- Initial velocity of particle B (u_B) = 10 m/s

2. **Understand the Nature of the Collision**:
- The collision is perfectly elastic, which means both momentum and kinetic energy are conserved.
- Since the masses are equal, we can use the property of elastic collisions for equal masses.

3. **Apply the Elastic Collision Formula**:
- For two objects of equal mass, the velocities after the collision can be determined by simply exchanging their velocities.
- Therefore, after the collision:
- Final velocity of particle A (v_A) = u_B = 10 m/s
- Final velocity of particle B (v_B) = u_A = 15 m/s

4. **State the Final Velocities**:
- The final velocities of the particles after the collision are:
- v_A = 10 m/s (for particle A)
- v_B = 15 m/s (for particle B)

5. **Conclusion**:
- The velocities of particles A and B after the collision are 10 m/s and 15 m/s, respectively.

### Final Answer:
The velocities after the elastic collision will be:
- Particle A: 10 m/s
- Particle B: 15 m/s