A rod of length 'l' is inclined at an angle `'theta'` with the floor against a smooth vertical wall. If the end A moves instantaneously with velocity `v_(1)`, what is the velocity of end B at the instant when rod makes `'theta'` angle with the horizontal.

Explanation

To solve the problem, we need to analyze the motion of the rod and use the relationship between the velocities of its ends based on the geometry of the situation.

### Step-by-Step Solution:

1. **Understand the Geometry**:
- We have a rod of length \( l \) inclined at an angle \( \theta \) with the horizontal. Let point A be at the bottom of the rod (on the floor) and point B be at the top (against the wall).
- The vertical wall is smooth, meaning there is no friction acting on the rod at point B.

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