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 different quantities involved in projectile motion.

### Step-by-Step Solution:

1. **Identify the quantities in projectile motion:**
- Kinetic Energy (KE)
- Momentum (p)
- Horizontal Velocity (Vx)
- Vertical Velocity (Vy)

2. **Analyze Kinetic Energy:**
- The formula for kinetic energy is given by:
\[ KE = \frac{1}{2} m v^2 \]
- As the projectile moves upward, its speed decreases due to the acceleration caused by gravity, and at the highest point, the vertical component of velocity becomes zero. Therefore, the kinetic energy changes throughout the motion.
- **Conclusion:** Kinetic Energy is not constant.

3. **Analyze Momentum:**
- Momentum is defined as:
\[ p = mv \]
- Since momentum is a vector quantity, both the magnitude and direction of velocity change during the projectile's motion (the vertical component changes while the horizontal component remains constant). Thus, the momentum also changes.
- **Conclusion:** Momentum is not constant.

4. **Analyze Horizontal Velocity:**
- The horizontal component of the initial velocity is given by:
\[ V_x = u \cos(\theta) \]
- In the absence of horizontal forces (assuming no air resistance), the horizontal velocity remains constant throughout the motion. There is no acceleration acting in the horizontal direction.
- **Conclusion:** Horizontal Velocity is constant.

5. **Analyze Vertical Velocity:**
- The vertical component of the initial velocity is given by:
\[ V_y = u \sin(\theta) \]
- The vertical velocity changes due to the acceleration of gravity acting downward. As the projectile rises, the vertical velocity decreases, and as it falls, it increases.
- **Conclusion:** Vertical Velocity is not constant.

### Final Answer:
The quantity that remains constant during the entire motion of a projectile is the **Horizontal Velocity**.

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