A particle A suffers an oblique elastic collision particle `B` that is at rest initially. If their masses with a are the same, then after the collision

Options

A. their `KE` may be equal
B. A continues to move in the original direction while `B` remains at rest
C. they will move in mutually perpendicular directions
D. A comes to rest and `B` starts rections moving in the direction of the original motion of `A2`

Explanation

To solve the problem of an oblique elastic collision between two particles A and B, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Scenario**:
- Particle A is moving with an initial velocity \( u \) and collides with particle B, which is initially at rest. Both particles have the same mass \( m \).

2. **Conservation of Momentum**:
- The principle of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
- The equation can be written as:
\[ m \cdot u + m \cdot 0 = m \cdot v_1 + m \cdot v_2 \]
- Simplifying this gives:
\[ mu = mv_1 + mv_2 \]
- Dividing through by \( m \) (since \( m \neq 0 \)):
\[ u = v_1 + v_2 \quad \text{(Equation 1)} \]

3. **Elastic Collision Condition**:
- In an elastic collision, the coefficient of restitution \( E \) is defined as the ratio of the relative velocity of separation to the relative velocity of approach.
- For this case, since \( E = 1 \):
\[ E = \frac{v_2 - v_1}{u} = 1 \]
- Rearranging gives:
\[ v_2 - v_1 = u \quad \text{(Equation 2)} \]

4. **Solving the Equations**:
- Now we have two equations:
1. \( v_1 + v_2 = u \)
2. \( v_2 - v_1 = u \)

- Adding these two equations:
\[ (v_1 + v_2) + (v_2 - v_1) = u + u \]
\[ 2v_2 = 2u \implies v_2 = u \]

- Substituting \( v_2 = u \) back into Equation 1:
\[ v_1 + u = u \implies v_1 = 0 \]

5. **Conclusion**:
- After the collision, particle A comes to rest (\( v_1 = 0 \)), and particle B moves with the velocity of particle A (\( v_2 = u \)). Therefore, particle B moves in the same direction as particle A was initially moving.

### Final Answer:
- Particle A comes to rest, and particle B moves in the direction of the original motion of particle A.