• Support PF! Buy your school textbooks, materials and every day products Here!

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
Homework Helper
Gold Member
3,631
701
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
Science Advisor
Homework Helper
Insights Author
Gold Member
32,535
4,975
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
Homework Helper
Insights Author
Gold Member
7,590
694
I would consider it in the reference frame of the ground. What ground effect does the river have?
 
  • #6
rude man
Homework Helper
Insights Author
Gold Member
7,590
694
what would B and C affect? Does it only affect how far down the river you go?
Getting very warm ....
 
  • #7
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728
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.]
 

Related Threads for: Least time for boat to cross (theory)

  • Last Post
Replies
5
Views
980
  • Last Post
Replies
1
Views
324
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
1
Views
4K
Replies
3
Views
1K
Replies
17
Views
3K
Replies
3
Views
3K
  • Last Post
Replies
2
Views
768
Top