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"In theory, theory and practice are the same. In practice, they are not." ..."Albert Einstein (1879~1955, Mathematical physicist, Nobel Prize 1921-Physics)"

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 Author Topic: Cross a river with a boat  (Read 4403 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
ahmedelshfie
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 « Embed this message on: March 10, 2011, 06:03:44 pm » posted from:Uberaba,Minas Gerais,Brazil

The applet design by prof Hwang, modified layout by Ahmed.
Original applet Cross a river with a boat

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, |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 θ + |vWL| .

Solving for θ, we find sinθ=|vWL|/|vBW|,
so θ =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 θ=c).
It will remember the last 3 traces.

Embed a running copy of this simulation

Embed a running copy link(show simulation in a popuped window)
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