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 about 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 is subject to the force of gravity. The motion can be analyzed in two dimensions: horizontal (x-direction) and vertical (y-direction).

2. **Identifying Forces**:
- In projectile motion, the only force acting on the object is the gravitational force, which acts downwards. This means that in the horizontal direction, there is no force acting on the projectile.

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

4. **Horizontal Motion**:
- Since there are no forces acting in the horizontal direction, the horizontal component of velocity \( u_x \) remains constant throughout the motion. Therefore, the horizontal velocity does not change.

5. **Vertical Motion**:
- In the vertical direction, the object is influenced by gravity, which causes the vertical component of velocity to change. As the object rises, the vertical velocity decreases until it reaches the maximum height, where it becomes zero, and then it increases again as it falls back down.

6. **Acceleration**:
- The acceleration due to gravity (g) acts downwards and remains constant throughout the motion. Thus, the vertical acceleration is unchanged.

7. **Kinetic Energy and Momentum**:
- Kinetic energy depends on the velocity of the object. Since the vertical velocity changes, the total kinetic energy of the projectile also changes as it moves up and down.
- Momentum, which is the product of mass and velocity, will also change because the vertical component of velocity is changing.

### Conclusion:
The quantities that remain unchanged during projectile motion are:
- Horizontal velocity (\( u \cos(\theta) \))
- Vertical acceleration (constant at \( g \))

### Final Answer:
The quantities that remain unchanged during projectile motion are:
1. Horizontal velocity
2. Vertical acceleration