From the top of the tower, two balls are thrown horizontally in opposite directions with velocities `u_(1)` and `u_(2)`. Find the distacne between the balls at the moment when their velocity vectors becomes mutually perpendicular. (Assume the height of tower very large)

Explanation

To solve the problem of finding the distance between two balls thrown horizontally from a tower when their velocity vectors become mutually perpendicular, we can follow these steps:

### Step 1: Understand the Motion of the Balls
Two balls are thrown horizontally from the top of a tower with initial velocities \( u_1 \) and \( u_2 \) in opposite directions. The motion of each ball can be analyzed separately.

### Step 2: Determine the Velocity Vectors
The velocity of each ball at time \( t \) can be expressed as:
- For the first ball (thrown with velocity \( u_1 \)):
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