During projectile motion,the quantities that remain unchanged are

Options

A. Force and vertical velocity
B. Acceleration and horizontal velocity
C. kinetic energy amd acceleration
D. Acceleration and momentum

Answer

To solve the question regarding the quantities that remain unchanged during projectile motion, we can analyze the motion step by step.

### Step-by-Step Solution:

1. **Understanding Projectile Motion**:
- Projectile motion occurs when an object is thrown into the air and moves under the influence of gravity. The motion can be analyzed in two dimensions: horizontal (x-direction) and vertical (y-direction).

2. **Identify Forces Acting on the Projectile**:
- The only force acting on the projectile during its flight is gravity, which acts downward with a force of \( mg \) (where \( m \) is the mass of the projectile and \( g \) is the acceleration due to gravity).

3. **Vertical Motion Analysis**:
- The vertical component of the initial velocity is given by \( u_y = u \sin \theta \).
- As the projectile rises, it decelerates due to gravity until it reaches its maximum height, where the vertical velocity becomes zero. After that, it accelerates downward.
- Therefore, the vertical velocity changes throughout the motion.

4. **Horizontal Motion Analysis**:
- The horizontal component of the initial velocity is given by \( u_x = u \cos \theta \).
- Since there are no horizontal forces acting on the projectile (assuming air resistance is negligible), the horizontal velocity remains constant throughout the motion.
- Thus, \( u_x \) does not change.

5. **Acceleration**:
- The acceleration in the vertical direction is constant and equal to \( -g \) (downward) throughout the motion.
- The horizontal acceleration is zero since there are no forces acting in that direction.

6. **Kinetic Energy**:
- Kinetic energy at any point is given by \( KE = \frac{1}{2} mv^2 \). Since the velocity changes during the projectile's flight, the kinetic energy also changes.

7. **Momentum**:
- Momentum is given by \( p = mv \). Since the velocity changes throughout the motion, the momentum also changes.

### Conclusion:
From the analysis, we find that the quantities that remain unchanged during projectile motion are:
- Horizontal velocity (remains constant)
- Vertical acceleration (remains constant at \( -g \))

Thus, the correct answer is that the quantities that remain unchanged are **horizontal velocity and vertical acceleration**.