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A man crosses the river in shortest time...

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:

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To solve the problem of a man crossing a river at an angle of \( \theta = 60^\circ \) to the direction of the water flow, we can follow these steps: ### Step 1: Understand the situation The man is crossing the river while the river is flowing. The speed of the river (water) is given as \( v_w = 4 \, \text{km/hr} \). The man crosses the river at an angle of \( 60^\circ \) to the direction of the flow. ### Step 2: Set up the relationship between the velocities We can use trigonometric relationships to relate the speed of the man (\( v_m \)) to the speed of the water. The horizontal component of the man's velocity must equal the speed of the water for him to reach the opposite bank at an angle. ...
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