Three swimmers who all swim at the same speed discuss how to cross a river in the shortest amount of time. Swimmer A will swim s
traight across the river at a right angle to the current. Swimmer B reasons that the current will carry A downstream, meaning that A will cover a greater distance to get across and therefore will take a longer time interval. B says he will aim at an upstream angle such that, allowing for the current, he will reach the other side directly across from where he starts, thus covering the shortest distance and arriving first. Swimmer C, reasoning that the time interval needed for B to cross will be longer than B expects because some of B’s effort will be spent battling the current, plans to aim at a downstream angle, so that the current assists rather than opposes him. This way he will be traveling at the highest speed and get across first. Which swimmer gets across first?
The time required for a swimmer to cross a river is equal to the width of the river which is divided by the magnitude of the component of the velocity which is parallel to the width of the river.
In the given context, all the three swimmers A, B and C swims in a different angle relative to the direction of the flow of river. The swimmer A swims straight at a direction perpendicular to the direction of current of the river across the width of the river, so A will have the largest velocity component which is parallel to the width of the river. So the time taken by swimmer A will be the least to cross the river.
