In case of a projectile motion, what is the angle between the velocity and acceleration at the highest point?

Options

A. `0^(@)`
B. `45^(@)`
C. `90^(@)`
D. `180^(@)`

Explanation

To solve the problem of finding the angle between the velocity and acceleration at the highest point of a projectile motion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Projectile Motion**:
- When a projectile is launched, it has both horizontal and vertical components of velocity. The initial velocity can be broken down into two components:
- Horizontal component: \( u \cos \theta \)
- Vertical component: \( u \sin \theta \)

2. **Analyzing the Highest Point**:
- At the highest point of the projectile's trajectory, the vertical component of the velocity becomes zero. This is because the projectile has reached its maximum height and is about to start descending.

3. **Velocity at the Highest Point**:
- At the highest point, the only component of velocity that remains is the horizontal component, which is \( u \cos \theta \). Thus, the velocity vector at this point is directed horizontally.

4. **Acceleration in Projectile Motion**:
- The only force acting on the projectile is gravity, which acts downwards. Therefore, the acceleration due to gravity is \( g \) and it acts vertically downward throughout the motion.

5. **Finding the Angle Between Velocity and Acceleration**:
- At the highest point, the velocity vector is horizontal (along the x-axis) and the acceleration vector (due to gravity) is vertical (along the y-axis).
- The angle between a horizontal line (velocity) and a vertical line (acceleration) is \( 90^\circ \).

6. **Conclusion**:
- Therefore, the angle between the velocity and acceleration at the highest point of a projectile motion is \( 90^\circ \).

### Final Answer:
The angle between the velocity and acceleration at the highest point of projectile motion is \( 90^\circ \).

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