Least time for boat to cross (theory)

[a lone fishy]

Homework Statement

[/B]
To cross a river with a current (flowing downstream) in the least amount of time, a boat should point

a) directly at the opposite shore
b) somewhat upstream
c) somewhat downstream
d) in a direction that will take the boat directly across
e) downstream

Homework Equations

The Attempt at a Solution

[/B]
I am aware that the only thing that affects time is the speed of the boat. I know E is wrong as well as D. I believe B and C are the same in terms of going upstream/downstream doesn't affect time. So i believe the answer could possibly be A

 

[epenguin]

So do I - it is easy to get distracted by other things you imagine you want, like shortest distance, or getting where you want but all that matters is your across rate, no matter what your down or upstream rate is.

 

[a lone fishy]

what would B and C affect? Does it only affect how far down the river you go?

 

[haruspex]

what would B and C affect? Does it only affect how far down the river you go?

Consider it in the reference frame of the water.

 

[rude man]

I would consider it in the reference frame of the ground. What ground effect does the river have?

 

[rude man]

what would B and C affect? Does it only affect how far down the river you go?

Getting very warm ...

 

[Ray Vickson]

I would consider it in the reference frame of the ground. What ground effect does the river have?

Your outboard motor propels the boat through the water at a constant, given speed with respect to the water the boat is floating in---that is, relative to the rest-frame of the water. For a given velocity vector (vx,vy) in the water's rest frame (where x = up/downstream direction and y = across/back direction), what is the ky-component (Vy) of velocity relative to the ground? How would you maximize Vy, subject to sqrt(vx^2 + vy^2) =constant? [Note, vy and Vy are different symbols.]