Two men `Pa n dQ` start with velocity `u` at the same time from the junction of two roads inclined at `45^0` to each other. If they travel by different roads, find the rate at which they are being separated.

Explanation

To solve the problem of finding the rate at which two men P and Q are being separated as they travel along two roads inclined at 45 degrees to each other, we can follow these steps:

### Step 1: Understanding the Problem
We have two men starting from the same point and moving away from each other along two roads that form a 45-degree angle. Both men have the same initial velocity, denoted as \( u \).

### Step 2: Representing Their Velocities
Let’s denote the velocity of man P as \( \mathbf{v_1} \) and the velocity of man Q as \( \mathbf{v_2} \). Since both men are moving at the same speed \( u \), we have:
- \( |\mathbf{v_1}| = u \)
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