Final answer:
The man must swim in a direction slightly upstream to counter the river current to reach a point directly opposite. The time required depends on his speed and the river's current speed. Without a current, it would take him approximately 9 minutes to cross a 600m wide river at a swimming speed of 1.11 m/s.
Step-by-step explanation:
To determine in what direction the man must swim to reach a point exactly opposite the starting point on the other side of the river, we need to understand the vector components of velocities. The man can swim at a speed of 4 km/h (approximately 1.11 m/s) relative to the water. If the river has a current, this will affect the direction in which he must swim. He must swim at an angle upstream to counteract the downstream current of the river. This will result in a diagonal path that ensures his resultant velocity is directly across to the opposite point.
The time it takes for the man to reach the opposite point will depend on the speed of the river's current. Working with a similar question provided as reference, where a boat attempts to travel straight across a river at a speed of 0.75 m/s and the current flows at 1.20 m/s, the directions and velocities must be combined using vector addition to find the resultant path and time to cross.
If the river current is zero or negligible, the man would need to swim directly across the river (perpendicular to the banks). Even in the absence of a current, the time to cross 600m at a swimming speed of 1.11 m/s would be calculated as follows: Time = Distance / Speed, which gives us approximately 540 seconds or 9 minutes to reach the opposite side.