Rain is falling vertically with velocity 10m /s and a man is moving with velocity `6 m s^-1`. Find the angle at which the man should hold his umbrella to above getting wet.

Explanation

To solve the problem of finding the angle at which a man should hold his umbrella to avoid getting wet from vertically falling rain, we can follow these steps:

### Step 1: Understand the given information
- The velocity of the rain (\(V_r\)) is \(10 \, \text{m/s}\) downward (which we can denote as negative in the vertical direction, i.e., \(-10 \hat{j}\)).
- The velocity of the man (\(V_m\)) is \(6 \, \text{m/s}\) horizontally (in the positive x-direction, i.e., \(6 \hat{i}\)).

### Step 2: Determine the relative velocity of the rain with respect to the man
The relative velocity of the rain with respect to the man (\(V_{rm}\)) can be calculated using the formula:
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