How should you travel across a flowing river in a boat to minimize your time of travel?
A) Straight across
B) Slightly upstream
C) Slightly downstream
D) The time will be independent of how you head
The Attempt at a Solution
I thought the time would always be independent of the direction because the x distance is constant whichever way you head. I was remembering a kinematics problem that is similar to this and I thought in that problem it didn't matter which way you headed.
But the answer is straight across, and while it makes sense because that is the shortest magnitude of the distance, I thought it would only depend on the horizontal component which is always the same. What am I not seeing?