NTNUJAVA Virtual Physics Laboratory
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Easy Java Simulations (2001- ) => kinematics => Topic started by: ahmedelshfie on March 10, 2011, 06:03:44 pm

Title: Cross a river with a boat
Post by: ahmedelshfie on March 10, 2011, 06:03:44 pm
The applet design by prof Hwang, modified layout by Ahmed.
Original applet Cross a river with a boat (http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=2125)

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.