A man swims across a river with speed of ` 5 km h^(-1)` ( in still water). While a boat goes upstream with speed ` 12 km h^(-1)` ( in still water). How fast and in which direction does, the man appear to go to the boatman ? Given that the speed of flowing water is ` 2 km h^(-1)`

Explanation

To solve the problem step by step, we will analyze the given information and apply vector addition to find the resultant velocity of the man as observed by the boatman.

### Step 1: Identify the velocities
- The speed of the man swimming across the river (in still water) is \( V_m = 5 \, \text{km/h} \).
- The speed of the boat going upstream (in still water) is \( V_b = 12 \, \text{km/h} \).
- The speed of the flowing water is \( V_w = 2 \, \text{km/h} \).

### Step 2: Determine the effective velocities
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