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. Fin dthe speed and direction of the rain with respedt to the road.

Explanation

To solve the problem, we need to analyze the situation using vector components. Let's denote:

- Speed of the man when he runs at 8 km/h: \( V_m1 = 8 \, \text{km/h} \)
- Speed of the man when he runs at 12 km/h: \( V_m2 = 12 \, \text{km/h} \)
- Speed of the rain: \( V_r \) (unknown)
- Angle of the rain with the vertical when the man runs at 12 km/h: \( \theta = 30^\circ \)

### Step-by-Step Solution:
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