A man running on the horizontal road at ` 8 km h^(-1)` find the rain appears to be falling vertically. He incresases his speed to `12 km h^(-1)` and find that the drops make angle ` 30^2` with the vertical. Find the speed and direction of the rain with respedt to the road.

Explanation

To solve the problem step by step, we will analyze the situation using the concepts of relative velocity and trigonometry.

### Step 1: Understand the initial conditions
The man is running at a speed of \( V_{m1} = 8 \, \text{km/h} \) and observes the rain falling vertically. This means that the horizontal component of the rain's velocity must equal the man's speed for the rain to appear vertical to him.

### Step 2: Set up the equations for the first scenario
Since the rain appears to fall vertically, we can conclude:
\[
...