A ball strikes a smooth horizontal floor obliquely and rebounds inelastically.

Options

A. The kinetic energy of the ball just after hitting the floor is equal to the potential energy of the ball at its maximum height alter rebound.
B. Total energy of the ball is not conserved.
C. The angle of rebound with the vertical is greater than the angle of incidence.
D. None of the above.

Explanation

To solve the problem of a ball striking a smooth horizontal floor obliquely and rebounding inelastically, we will analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Collision**:
- The ball strikes the floor at an angle, which means it has both horizontal and vertical components of velocity.
- The collision is inelastic, meaning that the ball does not retain all of its kinetic energy after the collision.

2. **Coefficient of Restitution**:
- The coefficient of restitution (e) is defined as the ratio of the relative velocity of separation to the relative velocity of approach.
- Since the collision is inelastic, the coefficient of restitution will be between 0 and 1 (0 < e < 1).

3. **Kinetic Energy Before and After Collision**:
- Before the collision, the kinetic energy (KE) of the ball can be expressed as:
\[ KE_{initial} = \frac{1}{2} m u^2 \]
- After the collision, the kinetic energy will be:
\[ KE_{final} = \frac{1}{2} m v^2 \]
- Due to the inelastic nature of the collision, some kinetic energy is transformed into other forms of energy (like sound, heat, etc.), so:
\[ KE_{final} < KE_{initial} \]

4. **Potential Energy at Maximum Height**:
- After rebounding, the ball will rise to a maximum height where its kinetic energy is converted into potential energy (PE). The potential energy at the maximum height (h) is given by:
\[ PE = mgh \]
- Since some kinetic energy is lost during the collision, the kinetic energy just after hitting the floor will not equal the potential energy at the maximum height.

5. **Conservation of Energy**:
- The total mechanical energy of the ball (kinetic + potential) is not conserved in this case because some energy is lost during the inelastic collision. Therefore, the statement that the total energy of the ball is conserved is incorrect.

6. **Angles of Incidence and Rebound**:
- The angle of incidence (α) is the angle at which the ball strikes the floor, and the angle of rebound (β) is the angle at which it leaves the floor.
- In an inelastic collision, the angle of rebound is typically greater than the angle of incidence due to the loss of energy and the change in momentum direction.

### Conclusion:
Based on the analysis:
- **Option A** is incorrect because the kinetic energy just after hitting the floor is not equal to the potential energy at the maximum height after rebound.
- **Option B** is correct because the total energy of the ball is not conserved during the inelastic collision.
- **Option C** is correct because the angle of rebound is greater than the angle of incidence in an inelastic collision.
- **Option D** is incorrect as there are correct options (B and C).

### Final Answer:
The correct options are **B** and **C**.

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