### Author Topic: Cross a river with a boat  (Read 38019 times)

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### Cross a river with a boat
« on: February 28, 2011, 05:00:05 pm »
You wish to cross a river and arrive at a dock that is directly across from you, but the river's current
will tend to carry you downstream. To compensate, you must steer the boat at an angle. Find the angle ?, given the magnitude, |vWL|, of the water's velocity relative to the land, and the maximum speed, |vBW|, of which the boat is capable relative to the water.

? The boat's velocity relative to the land equals the vector sum of its velocity with respect to the water and the water's velocity with respect to the land,
vBL = vBW+ vWL .

If the boat is to travel straight across the river, i.e., along the y axis, then we need to have vBL,x=0.
This x component equals the sum of the x components of the other two vectors,
vBL,x = vBW,x + vWL,x , or 0 = -|vBW| sin ? + |vWL| .

Solving for ?, we find sin?=|vWL|/|vBW|,
so ? =sin-1 |vWL|/|vBW|.

The following simulation let you play with it. Enjoy!

You can adjust the velocity of the river or the boat with slider.
You can also change it's direction (angle ?=c).
It will remember the last 3 traces.

Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
• Post questions to be asked to help students to think, to explore.
• Upload worksheets as attached files to share with more users.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### Re: Cross a river with a boat
« Reply #1 on: August 30, 2011, 11:08:42 am »
Here is another similar simulation.
You can play with 5 boats at a time. Enjoy it!

You can change river flow speed by drag red arrow horizontally (center of simulation region).
You can change the moving direction of each boat by dragging velocity arrow for each boat.
Click show will show actual moving direction.
Drag the rectangle dot can move boats in horizontal direction.
Click start button to drive boats.

Which boat will move to the other side with shortest travel time?
Which boat will move to the other side with shortest travel distance?
What is the trajectory for each boat?

Try to write down your answer before you click start button. (click init button to play it again).

Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
• Post questions to be asked to help students to think, to explore.
• Upload worksheets as attached files to share with more users.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!

#### BlueLotus

• Newbie
• Posts: 2
##### Re: Cross a river with a boat
« Reply #2 on: November 07, 2013, 07:35:02 pm »
I have learned in the schools about relative velocity and that is always a tough topic to me. Physics was my favorite subject, still sometimes I used to get confused between velocity, area etc. The way you handled this issue really impressed me. Good work man!

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#### ymbeste

• Newbie
• Posts: 1
##### Re: Cross a river with a boat
« Reply #3 on: June 11, 2016, 03:55:47 am »
It is a superb topic.

I like it.

#### rockmanx4

• Newbie
• Posts: 1
##### Re: Cross a river with a boat
« Reply #4 on: July 12, 2016, 01:16:16 am »
it good content