Physics Principles and Problems 2009

Chapter 3: Accelerated Motion

Problem of the Week

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Sailing
An amateur yachtsman who is also a physicist has worked out the mathematics for determining the fastest route for sailing from point A to point B. The figure below is a vector diagram that shows all the possible velocities for a given wind direction.
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0078807220/193800/ch04_sailing.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (11.0K)</a>Sailing directly into the wind is impossible, and sailing directly with the wind is not the fastest way to go.

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Fastest Path from Point A to Point B
To use the vector diagram to work out the best route, follow these three steps:
  1. Draw the vector diagram with the axis of symmetry in the direction of the wind.
  2. Draw the line from the starting point A to the destination point B, a.k.a. the slowness vector.
  3. At right angles to the slowness vector, draw a line that just touches the velocity arc.
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The intersection of the right-angle line and the velocity arc determines the best direction to aim from point A. Of course this direction will change as the slowness vector changes, so you will need to continually recalculate a new heading.
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0078807220/193800/POWproblem1.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> Determine the route a sailboat might take from point A to point B and then from point B to point C.

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<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0078807220/193800/webLinks.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> See it on the web:
http://www.newscientist.com/ns/980228/
nsailing.html
Clicking will launch a new window.
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