What Is the Fastest Way to Cross a Flowing River by Boat?

[rasen58]

Homework Statement

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

Homework Equations

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?

 

[jbriggs444]

The x component of distance is constant regardless of which way you head. But is the x component of your velocity constant?

 

[rasen58]

Why wouldn't it be constant if it's not accelerating in the x direction since its traveling perpendicular to the river current?

 

[jbriggs444]

My apologies for writing confusingly.

The x component of velocity will be constant for any given angle. But it will not be the same for each angle.

 

[rasen58]

Oh I see, I guess that's true. Only if you go straight across will you have the greatest horizontal velocity.

 

[haruspex]

How should you travel across a flowing river

This is quite ambiguous. Does it mean relative to the water (i.e. which way should you point the boat) or relative to the shore?