A ball is thrown at a certain angle with the horizontal and it returns to the ground describing a parabolic path. Which of the following remains constant?

Options

A. Momentum of the ball
B. Kinetic energy of the ball
C. Vertical component of the velocity
D. Horizontal component of the velocity

Answer

To solve the problem, we need to analyze the motion of the ball thrown at an angle with the horizontal. The key points to consider are the components of the velocity and how they change during the motion.

### Step-by-Step Solution:

1. **Understanding the Motion**:
- When a ball is thrown at an angle (let's call it θ) with an initial velocity (v), it follows a parabolic trajectory due to the influence of gravity.

2. **Breaking Down the Velocity**:
- The initial velocity can be broken down into two components:
- Horizontal component: \( V_x = v \cos \theta \)
- Vertical component: \( V_y = v \sin \theta \)

3. **Analyzing the Horizontal Motion**:
- In the horizontal direction, there are no external forces acting on the ball (assuming air resistance is negligible). Therefore, the horizontal component of velocity \( V_x \) remains constant throughout the motion.

4. **Analyzing the Vertical Motion**:
- In the vertical direction, the ball is influenced by gravity. The vertical component of velocity \( V_y \) changes continuously due to gravitational acceleration (g). As the ball rises, \( V_y \) decreases until it reaches the peak, and then it increases again as the ball falls back down.

5. **Considering Momentum**:
- The momentum of the ball is given by \( p = m \cdot v \), where \( v \) is the total velocity. Since \( V_y \) changes, the total momentum will also change throughout the motion.

6. **Considering Kinetic Energy**:
- The kinetic energy of the ball is given by \( KE = \frac{1}{2} m v^2 \). Since the total velocity \( v \) changes (because \( V_y \) changes), the kinetic energy will also change.

7. **Conclusion**:
- The only quantity that remains constant during the entire parabolic motion is the horizontal component of the velocity \( V_x \).

### Final Answer:
The horizontal component of the velocity \( V_x \) remains constant.

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