Assertion: In case of projectile motion, acceleration horizontal component of velocity and mechanical energy remains unchanged but speed. Vertical component of velocity, momentum K.E. and P.E. change.
Reason: In the presence of air resistance, the range and maximum height attained reduce, but time of flight increases.

Options

A. both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.
B. If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.
C. If Assertion is Trie but the Reason is False.
D. If both Assertion `&` Reason are false

Answer

To analyze the given assertion and reason, we will break down the concepts of projectile motion and the effects of air resistance step by step.

### Step 1: Understanding Projectile Motion
In projectile motion, an object is launched at an angle with an initial velocity. The motion can be separated into horizontal and vertical components:
- **Horizontal Component (x-direction)**:
- Initial velocity: \( V_x = V \cos(\theta) \)
- Acceleration: \( a_x = 0 \) (no horizontal forces acting)
- Therefore, horizontal velocity remains constant: \( V_x = V \cos(\theta) \)

- **Vertical Component (y-direction)**:
- Initial velocity: \( V_y = V \sin(\theta) \)
- Acceleration: \( a_y = -g \) (gravity acts downwards)
- Vertical velocity changes over time due to gravity.

### Step 2: Analyzing the Assertion
The assertion states:
1. The horizontal component of velocity remains unchanged.
2. Mechanical energy remains unchanged.
3. Speed, vertical component of velocity, momentum, kinetic energy, and potential energy change.

**Analysis**:
- **Horizontal Component of Velocity**: True, as there is no horizontal acceleration.
- **Mechanical Energy**: In the absence of air resistance, mechanical energy (sum of kinetic and potential energy) remains constant because gravity is a conservative force.
- **Vertical Component of Velocity**: True, it changes due to the acceleration from gravity.
- **Speed**: True, as speed is the magnitude of velocity, which changes due to the changing vertical component.
- **Momentum**: True, as vertical momentum changes due to the force of gravity.
- **Kinetic Energy (K.E.) and Potential Energy (P.E.)**: Both change as the projectile moves up and down.

Thus, the assertion is **true**.

### Step 3: Analyzing the Reason
The reason states:
- In the presence of air resistance, the range and maximum height attained reduce, but the time of flight increases.

**Analysis**:
- **Range and Maximum Height**: True, air resistance opposes the motion, reducing both the range and maximum height.
- **Time of Flight**: This part is **false**. Air resistance actually decreases the time of flight because it slows down the ascent and descent, leading to a shorter overall flight time.

### Conclusion
- **Assertion**: True
- **Reason**: False

### Final Answer
The assertion is true, but the reason is false.