# Least time for boat to cross (theory)

1. Dec 10, 2015

### a lone fishy

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

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 doesnt affect time. So i believe the answer could possibly be A

2. Dec 10, 2015

### 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.

3. Dec 10, 2015

### a lone fishy

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

4. Dec 10, 2015

### haruspex

Consider it in the reference frame of the water.

5. Dec 12, 2015

### rude man

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

6. Dec 12, 2015

### rude man

Getting very warm ....

7. Dec 12, 2015

### Ray Vickson

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 = accross/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.]