Cross a river with a boat

[Fu-Kwun Hwang]

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 θ, given the magnitude, |v_WL|, of the water's velocity relative to the land, and the maximum speed, |v_BW|, 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,
v_BL = v_BW+ v_WL .

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

Solving for θ, we find sinθ=|v_WL|/|v_BW|,
 so θ =sin^-1 |v_WL|/|v_BW|.

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 θ=c).
It will remember the last 3 traces.

Embed a running copy of this simulation
<applet code='users.ntnu.fkh.motion_boatNriver_pkg.motion_boatNriverApplet.class' archive='http://www.phy.ntnu.edu.tw/ntnujava/ejsuser/2/ejs_motion_boatNriver.jar' name='motion_boatNriver7926' id='motion_boatNriver7926' width='647' height='379' mayscript=true><param name='draggable' value='true'></applet>
Embed a running copy link(show simulation in a popuped window)
<a href='http://www.phy.ntnu.edu.tw/ntnujava/msg.php?smfejs=7926' target='smfejs'>Run simulation</a>

Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

• 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]

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.

Questions to be asked:
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).

Embed a running copy of this simulation
<applet code='users.ntnu.fkh.boatcrossriver_pkg.boatcrossriverApplet.class' archive='http://www.phy.ntnu.edu.tw/ntnujava/ejsuser/2/ejs_boatcrossriver.jar' name='boatcrossriver8515' id='boatcrossriver8515' width='677' height='383' mayscript=true><param name='draggable' value='true'></applet>
Embed a running copy link(show simulation in a popuped window)
<a href='http://www.phy.ntnu.edu.tw/ntnujava/msg.php?smfejs=8515' target='smfejs'>Run simulation</a>

Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

• 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]

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]

It is a superb topic.

I like it.

[rockmanx4]

it good content