A point mass is projected, making an acute angle with the horizontal. If angle between velocity `overset(rarr)v` and acceleration `overset(rarr)g` is `theta` then `theta` is given by

Options

A. `0^(@) < theta < 90^(@)`
B. `theta=90^(@)`
C. `theta=90^(@)`
D. `90^(@) < theta < 180^(@)`

Answer

To solve the problem, we need to determine the angle \( \theta \) between the velocity vector \( \vec{v} \) of a projectile and the acceleration vector \( \vec{g} \) due to gravity.

### Step-by-Step Solution:

1. **Understanding the Vectors**:
- When a projectile is launched at an acute angle to the horizontal, it has an initial velocity \( \vec{v} \) that can be broken down into horizontal and vertical components.
- The acceleration due to gravity \( \vec{g} \) acts vertically downward.

2. **Identifying the Angle**:
- The angle \( \theta \) is defined as the angle between the velocity vector \( \vec{v} \) and the acceleration vector \( \vec{g} \).
- Since \( \vec{g} \) is directed downward, the angle \( \theta \) will be measured from the direction of \( \vec{v} \) to \( \vec{g} \).

3. **Analyzing the Motion**:
- As the projectile moves upward, the vertical component of its velocity decreases due to the downward acceleration \( \vec{g} \).
- At the peak of its trajectory, the vertical component of the velocity becomes zero, and the projectile starts descending.

4. **Determining the Range of \( \theta \)**:
- When the projectile is launched, the angle \( \theta \) between \( \vec{v} \) and \( \vec{g} \) will be acute (less than 90 degrees) while it is ascending.
- At the peak, \( \theta \) becomes 90 degrees as the velocity vector is horizontal.
- As the projectile descends, \( \theta \) will again be acute but greater than 90 degrees when measured from the upward velocity to the downward acceleration.

5. **Conclusion**:
- Hence, the angle \( \theta \) between the velocity \( \vec{v} \) and the acceleration \( \vec{g} \) will always be greater than 90 degrees and less than 180 degrees during the projectile motion.

### Final Answer:
The angle \( \theta \) is given by:
\[ 90^\circ < \theta < 180^\circ \]