If a body is projected with an angle `theta` to the horizontal, then

Options

A. its velocity is always perpendicular to its acceleration then
B. its velocity becomes zero at its maximum height.
C. its velocity makes zero angle with the horizontal at its maximum height.
D. the body just before hitting the ground, the direction of velocity coincides with the acceleration.

Explanation

To solve the question regarding the projectile motion of a body projected at an angle θ to the horizontal, we will analyze each of the given options step by step.

### Step-by-Step Solution:

1. **Understanding Projectile Motion**:
- When a body is projected at an angle θ, it has two components of velocity:
- Horizontal component: \( u_x = u \cos \theta \)
- Vertical component: \( u_y = u \sin \theta \)
- The only acceleration acting on the body is due to gravity, which acts vertically downward with a magnitude of \( g \).

2. **Analyzing Option 1**:
- The statement claims that the velocity is always perpendicular to the acceleration.
- This is incorrect. At the moment of projection, the velocity has both horizontal and vertical components, and the acceleration due to gravity acts downward. The angle between the velocity and acceleration is not always 90 degrees.
- **Conclusion**: Option 1 is incorrect.

3. **Analyzing Option 2**:
- The statement claims that the velocity becomes zero at its maximum height.
- At maximum height, the vertical component of velocity (\( u_y \)) becomes zero, but the horizontal component (\( u_x \)) remains constant. Therefore, the total velocity does not become zero.
- **Conclusion**: Option 2 is incorrect.

4. **Analyzing Option 3**:
- The statement claims that the velocity makes a zero angle with the horizontal at its maximum height.
- At maximum height, the vertical component of the velocity is zero, and only the horizontal component remains. Thus, the velocity vector is horizontal, making a zero-degree angle with the horizontal.
- **Conclusion**: Option 3 is correct.

5. **Analyzing Option 4**:
- The statement claims that just before hitting the ground, the direction of velocity coincides with the acceleration.
- Just before impact, the velocity has both horizontal and vertical components. The acceleration due to gravity acts vertically downward. Therefore, the velocity vector does not coincide with the direction of acceleration, as there is still a horizontal component present.
- **Conclusion**: Option 4 is incorrect.

### Final Answer:
The only correct option is **Option 3**: The velocity makes a zero angle with the horizontal at its maximum height.

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