A man can walk on the shore at a speed `v_1` = 6 km/hr & swim in still water with a speed `V_2` = 5 km/hr. If the speed of water is `V_3` = 4 km/hr, at what angle should he head in the river in order to reach the exactly opposite point of the other shore in "shortest time including his swimming & walking?

Explanation

To solve the problem, we need to determine the angle at which the man should head in the river to reach the opposite shore in the shortest time. Here’s a step-by-step solution:

### Step 1: Understand the scenario
The man can walk on the shore at a speed \( v_1 = 6 \, \text{km/hr} \) and swim in still water at a speed \( v_2 = 5 \, \text{km/hr} \). The river has a current with a speed \( v_3 = 4 \, \text{km/hr} \).

### Step 2: Set up the coordinate system
Assume the river flows from left to right. The man starts at point A on the left bank and wants to reach point B directly opposite on the right bank.

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