A man crosses the river in shortest time and reaches at an angle `theta= 60^(@)` to the direction of flow of water. If the speed of water is `v_w = 4 km//hr`, find the speed of the man:

Explanation

To solve the problem of a man crossing a river in the shortest time while reaching at an angle of \( \theta = 60^\circ \) to the direction of the water flow, we can use the concept of relative velocity. Here’s a step-by-step solution:

### Step 1: Understand the scenario
The man swims across the river, and the river flows with a velocity \( v_w = 4 \, \text{km/hr} \). The angle \( \theta = 60^\circ \) indicates the direction of the man's resultant velocity with respect to the flow of the river.

### Step 2: Set up the velocity components
Let:
- \( v_m \) = speed of the man with respect to water (what we need to find).
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