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.

**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

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