Final answer:
The minimum time to cross a river for a swimmer not accounting for the current would depend on the swimmer's speed and the width of the river. Without the width provided, the crossing time cannot be calculated. The distance covered downstream is irrelevant to the time taken to swim directly across.
Step-by-step explanation:
The question of how an individual can cross a river at the minimum time involves understanding the concept of relative motion in Physics. Since the person can swim at a speed of 10 meters per second relative to the river, and the river is flowing at a speed of 5 meters per second, the total speed of the swimmer with respect to the ground is the vector sum of these two speeds. However, to minimize the time taken to cross the river, the swimmer should aim to swim directly across the river, which means he should not try to counteract the river's downstream flow.
To determine how long it takes to cross the river, one would typically need to know the river's width. Since the width of the river isn't given in the question, we cannot calculate the time taken to cross it. Nevertheless, assuming the width of the river remains constant, the minimum time will be achieved by swimming across the river at the swimmer's maximum speed relative to the water, without any horizontal displacement due to the river's current. The width of the river does not affect the minimum time as it's a fixed distance that needs to be covered at maximum speed perpendicularly.
The original question asked about a person who wants to cross the river in the minimum time, but without the width provided, it's impossible to calculate the time needed for the crossing. The details pertaining to crossing times and distances in other examples are only related if the width of the river is known.