Least time for boat to cross (theory)

  • #1

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

 

Answers and Replies

  • #2
epenguin
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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
what would B and C affect? Does it only affect how far down the river you go?
 
  • #4
haruspex
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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.
 
  • #5
rude man
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I would consider it in the reference frame of the ground. What ground effect does the river have?
 
  • #7
Ray Vickson
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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 = 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.]
 

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