will tend to carry you downstream. To compensate, you must steer the boat at an angle. Find the angle ?, given the magnitude, |v[sub]WL[/sub]|, of the water's velocity relative to the land, and the maximum speed, |v[sub]BW[/sub]|, 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[sub]BL[/sub] = v[sub]BW[/sub]+ v[sub]WL[/sub] .

If the boat is to travel straight across the river, i.e., along the y axis, then we need to have v[sub]BL[/sub],x=0.

This x component equals the sum of the x components of the other two vectors,

v[sub]BL,x[/sub] = v[sub]BW,x[/sub] + v[sub]WL,x[/sub] , or 0 = -|v[sub]BW[/sub]| sin ? + |v[sub]WL[/sub]| .

Solving for ?, we find sin?=|v[sub]WL[/sub]|/|v[sub]BW[/sub]|,

so ? =sin[sup]-1[/sup] |v[sub]WL[/sub]|/|v[sub]BW[/sub]|.

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.translate strings in simulation to different language format before download

Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list

Download EJS jar file(1024.8kB):double click downloaded file to run it. (67 times by 45 users) , Download EJS source View EJS source