Problem
Problem
A man who can swim at a velocity relative to water wants to cross a river of width , flowing with a speed . a. The minimum time in which he can cross the river is b. He can reach a point exactly opposite on the bank in time if c. He cannot reach the point exactly opposite on the bank if d. He cannot reach the point exactly opposite on the bank ifIntuitive explanation
The key is understanding vector addition of velocities: your swimming speed relative to the water and the river's current are independent, and they add as vectors to give your actual motion relative to the ground. Depending on your swimming direction, you can minimize crossing time (aim straight across and drift downstream) or reach a specific point directly opposite (angle upstream to cancel the current). Think about which component of your velocity actually gets you across the river versus which gets swept along it.
Intuitive explanation
The key is understanding vector addition of velocities: your swimming speed relative to the water and the river's current are independent, and they add as vectors to give your actual motion relative to the ground. Depending on your swimming direction, you can minimize crossing time (aim straight across and drift downstream) or reach a specific point directly opposite (angle upstream to cancel the current). Think about which component of your velocity actually gets you across the river versus which gets swept along it.