Which quantity associated with the projectile motion remains constant during entire motion?

Options

A. kinetic energy
B. momentum
C. horizontal velocity
D. vertical velocity

Answer

To determine which quantity associated with projectile motion remains constant throughout the entire motion, we can analyze the motion in both the horizontal and vertical directions.

### Step-by-Step Solution:

1. **Understanding Projectile Motion**:
- Projectile motion occurs when an object is thrown into the air with an initial velocity at an angle to the horizontal. The motion can be analyzed in two dimensions: horizontal (x-axis) and vertical (y-axis).

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

3. **Acceleration in Different Directions**:
- In the horizontal direction (x-axis), there is no acceleration acting on the projectile (assuming air resistance is negligible). Therefore, the horizontal velocity remains constant.
- In the vertical direction (y-axis), the only acceleration acting on the projectile is due to gravity, which is directed downward with a magnitude of \( g \).

4. **Conclusion About Horizontal Velocity**:
- Since there is no acceleration in the horizontal direction, the horizontal component of velocity \( u_x = u \cos \theta \) remains constant throughout the motion.
- In contrast, the vertical component of velocity changes due to the acceleration from gravity.

5. **Final Answer**:
- The quantity that remains constant during the entire projectile motion is the horizontal velocity.