Two stones are projected simultaneously from a tower a differenct angles of projection with same speed `'u'`. The distance between two stones is increasing at constant rate `'u'`. Then the angle between the initial velocity vectors of the two stones is `:`

Options

A. `30^(@)`
B. `60^(@)`
C. `45^(@)`
D. `90^(@)`

Explanation

To solve the problem, we need to analyze the motion of the two stones projected from the tower at different angles but with the same speed `u`. The key points to consider are the horizontal and vertical components of their velocities and how the distance between them changes over time.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Two stones are projected from the same point with the same speed `u` but at different angles, say θ₁ and θ₂.
- The distance between the two stones is increasing at a constant rate of `u`.

2. **Velocity Components**:
- The horizontal component of the velocity for the first stone (angle θ₁) is:
\[ u_x1 = u \cos(θ₁) \]
- The horizontal component of the velocity for the second stone (angle θ₂) is:
\[ u_x2 = u \cos(θ₂) \]

3. **Relative Velocity**:
- The relative horizontal velocity between the two stones is:
\[ u_{rel} = u_x1 - u_x2 = u \cos(θ₁) - u \cos(θ₂) \]

4. **Distance Between Stones**:
- The distance between the two stones is given by `l`, and the rate of change of this distance is given as:
\[ \frac{dl}{dt} = u \]

5. **Setting Up the Equation**:
- Since the distance is increasing at a constant rate, we can equate the relative horizontal velocity to the rate of change of distance:
\[ u \cos(θ₁) - u \cos(θ₂) = u \]

6. **Simplifying the Equation**:
- Dividing through by `u` (assuming `u ≠ 0`):
\[ \cos(θ₁) - \cos(θ₂) = 1 \]

7. **Using Trigonometric Identity**:
- Rearranging gives:
\[ \cos(θ₁) - 1 = \cos(θ₂) \]
- This implies that:
\[ \cos(θ₁) = 1 + \cos(θ₂) \]

8. **Finding the Angles**:
- The only way for the cosine of an angle to be greater than 1 is if the angle is 0 degrees. However, since we are looking for the angle between the two stones, we can use the fact that the two angles must be complementary in a way that they form an equilateral triangle.

9. **Conclusion**:
- Since the distance between the two stones is increasing at a constant rate, the angle between their initial velocity vectors must be 60 degrees, as this is the only configuration that maintains a constant distance while both stones are projected at the same speed.

### Final Answer:
The angle between the initial velocity vectors of the two stones is **60 degrees**.